Some supercongruences occurring in truncated hypergeometric series
For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hy...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Long, Ling [verfasserIn] |
|---|
| Format: |
E-Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2016transfer abstract |
|---|
| Schlagwörter: |
|---|
| Umfang: |
36 |
|---|
| Übergeordnetes Werk: |
Enthalten in: Evidence of Titan’s climate history from evaporite distribution - MacKenzie, Shannon M. ELSEVIER, 2014, Amsterdam [u.a.] |
|---|---|
| Übergeordnetes Werk: |
volume:290 ; year:2016 ; day:26 ; month:02 ; pages:773-808 ; extent:36 |
| Links: |
|---|
| DOI / URN: |
10.1016/j.aim.2015.11.043 |
|---|
| Katalog-ID: |
ELV035552050 |
|---|
| LEADER | 01000caa a22002652 4500 | ||
|---|---|---|---|
| 001 | ELV035552050 | ||
| 003 | DE-627 | ||
| 005 | 20230625204651.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 180603s2016 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1016/j.aim.2015.11.043 |2 doi | |
| 028 | 5 | 2 | |a GBVA2016020000011.pica |
| 035 | |a (DE-627)ELV035552050 | ||
| 035 | |a (ELSEVIER)S0001-8708(15)00521-6 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 082 | 0 | |a 510 | |
| 082 | 0 | 4 | |a 510 |q DE-600 |
| 082 | 0 | 4 | |a 520 |q VZ |
| 082 | 0 | 4 | |a 530 |q VZ |
| 082 | 0 | 4 | |a 570 |q VZ |
| 084 | |a BIODIV |q DE-30 |2 fid | ||
| 084 | |a 44.94 |2 bkl | ||
| 100 | 1 | |a Long, Ling |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Some supercongruences occurring in truncated hypergeometric series |
| 264 | 1 | |c 2016transfer abstract | |
| 300 | |a 36 | ||
| 336 | |a nicht spezifiziert |b zzz |2 rdacontent | ||
| 337 | |a nicht spezifiziert |b z |2 rdamedia | ||
| 338 | |a nicht spezifiziert |b zu |2 rdacarrier | ||
| 520 | |a For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. | ||
| 520 | |a For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. | ||
| 650 | 7 | |a Hypergeometric series |2 Elsevier | |
| 650 | 7 | |a Supercongruences |2 Elsevier | |
| 650 | 7 | |a p-adic Gamma functions |2 Elsevier | |
| 700 | 1 | |a Ramakrishna, Ravi |4 oth | |
| 773 | 0 | 8 | |i Enthalten in |n Elsevier |a MacKenzie, Shannon M. ELSEVIER |t Evidence of Titan’s climate history from evaporite distribution |d 2014 |g Amsterdam [u.a.] |w (DE-627)ELV012586625 |
| 773 | 1 | 8 | |g volume:290 |g year:2016 |g day:26 |g month:02 |g pages:773-808 |g extent:36 |
| 856 | 4 | 0 | |u https://doi.org/10.1016/j.aim.2015.11.043 |3 Volltext |
| 912 | |a GBV_USEFLAG_U | ||
| 912 | |a GBV_ELV | ||
| 912 | |a SYSFLAG_U | ||
| 912 | |a FID-BIODIV | ||
| 912 | |a SSG-OLC-PHA | ||
| 912 | |a GBV_ILN_22 | ||
| 912 | |a GBV_ILN_359 | ||
| 936 | b | k | |a 44.94 |j Hals-Nasen-Ohrenheilkunde |q VZ |
| 951 | |a AR | ||
| 952 | |d 290 |j 2016 |b 26 |c 0226 |h 773-808 |g 36 | ||
| 953 | |2 045F |a 510 | ||
| author_variant |
l l ll |
|---|---|
| matchkey_str |
longlingramakrishnaravi:2016----:oeuecnrecscurnituctdye |
| hierarchy_sort_str |
2016transfer abstract |
| bklnumber |
44.94 |
| publishDate |
2016 |
| allfields |
10.1016/j.aim.2015.11.043 doi GBVA2016020000011.pica (DE-627)ELV035552050 (ELSEVIER)S0001-8708(15)00521-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 520 VZ 530 VZ 570 VZ BIODIV DE-30 fid 44.94 bkl Long, Ling verfasserin aut Some supercongruences occurring in truncated hypergeometric series 2016transfer abstract 36 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. Hypergeometric series Elsevier Supercongruences Elsevier p-adic Gamma functions Elsevier Ramakrishna, Ravi oth Enthalten in Elsevier MacKenzie, Shannon M. ELSEVIER Evidence of Titan’s climate history from evaporite distribution 2014 Amsterdam [u.a.] (DE-627)ELV012586625 volume:290 year:2016 day:26 month:02 pages:773-808 extent:36 https://doi.org/10.1016/j.aim.2015.11.043 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA GBV_ILN_22 GBV_ILN_359 44.94 Hals-Nasen-Ohrenheilkunde VZ AR 290 2016 26 0226 773-808 36 045F 510 |
| spelling |
10.1016/j.aim.2015.11.043 doi GBVA2016020000011.pica (DE-627)ELV035552050 (ELSEVIER)S0001-8708(15)00521-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 520 VZ 530 VZ 570 VZ BIODIV DE-30 fid 44.94 bkl Long, Ling verfasserin aut Some supercongruences occurring in truncated hypergeometric series 2016transfer abstract 36 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. Hypergeometric series Elsevier Supercongruences Elsevier p-adic Gamma functions Elsevier Ramakrishna, Ravi oth Enthalten in Elsevier MacKenzie, Shannon M. ELSEVIER Evidence of Titan’s climate history from evaporite distribution 2014 Amsterdam [u.a.] (DE-627)ELV012586625 volume:290 year:2016 day:26 month:02 pages:773-808 extent:36 https://doi.org/10.1016/j.aim.2015.11.043 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA GBV_ILN_22 GBV_ILN_359 44.94 Hals-Nasen-Ohrenheilkunde VZ AR 290 2016 26 0226 773-808 36 045F 510 |
| allfields_unstemmed |
10.1016/j.aim.2015.11.043 doi GBVA2016020000011.pica (DE-627)ELV035552050 (ELSEVIER)S0001-8708(15)00521-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 520 VZ 530 VZ 570 VZ BIODIV DE-30 fid 44.94 bkl Long, Ling verfasserin aut Some supercongruences occurring in truncated hypergeometric series 2016transfer abstract 36 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. Hypergeometric series Elsevier Supercongruences Elsevier p-adic Gamma functions Elsevier Ramakrishna, Ravi oth Enthalten in Elsevier MacKenzie, Shannon M. ELSEVIER Evidence of Titan’s climate history from evaporite distribution 2014 Amsterdam [u.a.] (DE-627)ELV012586625 volume:290 year:2016 day:26 month:02 pages:773-808 extent:36 https://doi.org/10.1016/j.aim.2015.11.043 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA GBV_ILN_22 GBV_ILN_359 44.94 Hals-Nasen-Ohrenheilkunde VZ AR 290 2016 26 0226 773-808 36 045F 510 |
| allfieldsGer |
10.1016/j.aim.2015.11.043 doi GBVA2016020000011.pica (DE-627)ELV035552050 (ELSEVIER)S0001-8708(15)00521-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 520 VZ 530 VZ 570 VZ BIODIV DE-30 fid 44.94 bkl Long, Ling verfasserin aut Some supercongruences occurring in truncated hypergeometric series 2016transfer abstract 36 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. Hypergeometric series Elsevier Supercongruences Elsevier p-adic Gamma functions Elsevier Ramakrishna, Ravi oth Enthalten in Elsevier MacKenzie, Shannon M. ELSEVIER Evidence of Titan’s climate history from evaporite distribution 2014 Amsterdam [u.a.] (DE-627)ELV012586625 volume:290 year:2016 day:26 month:02 pages:773-808 extent:36 https://doi.org/10.1016/j.aim.2015.11.043 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA GBV_ILN_22 GBV_ILN_359 44.94 Hals-Nasen-Ohrenheilkunde VZ AR 290 2016 26 0226 773-808 36 045F 510 |
| allfieldsSound |
10.1016/j.aim.2015.11.043 doi GBVA2016020000011.pica (DE-627)ELV035552050 (ELSEVIER)S0001-8708(15)00521-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 520 VZ 530 VZ 570 VZ BIODIV DE-30 fid 44.94 bkl Long, Ling verfasserin aut Some supercongruences occurring in truncated hypergeometric series 2016transfer abstract 36 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. Hypergeometric series Elsevier Supercongruences Elsevier p-adic Gamma functions Elsevier Ramakrishna, Ravi oth Enthalten in Elsevier MacKenzie, Shannon M. ELSEVIER Evidence of Titan’s climate history from evaporite distribution 2014 Amsterdam [u.a.] (DE-627)ELV012586625 volume:290 year:2016 day:26 month:02 pages:773-808 extent:36 https://doi.org/10.1016/j.aim.2015.11.043 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA GBV_ILN_22 GBV_ILN_359 44.94 Hals-Nasen-Ohrenheilkunde VZ AR 290 2016 26 0226 773-808 36 045F 510 |
| language |
English |
| source |
Enthalten in Evidence of Titan’s climate history from evaporite distribution Amsterdam [u.a.] volume:290 year:2016 day:26 month:02 pages:773-808 extent:36 |
| sourceStr |
Enthalten in Evidence of Titan’s climate history from evaporite distribution Amsterdam [u.a.] volume:290 year:2016 day:26 month:02 pages:773-808 extent:36 |
| format_phy_str_mv |
Article |
| bklname |
Hals-Nasen-Ohrenheilkunde |
| institution |
findex.gbv.de |
| topic_facet |
Hypergeometric series Supercongruences p-adic Gamma functions |
| dewey-raw |
510 |
| isfreeaccess_bool |
false |
| container_title |
Evidence of Titan’s climate history from evaporite distribution |
| authorswithroles_txt_mv |
Long, Ling @@aut@@ Ramakrishna, Ravi @@oth@@ |
| publishDateDaySort_date |
2016-01-26T00:00:00Z |
| hierarchy_top_id |
ELV012586625 |
| dewey-sort |
3510 |
| id |
ELV035552050 |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">ELV035552050</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230625204651.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">180603s2016 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.aim.2015.11.043</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">GBVA2016020000011.pica</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV035552050</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0001-8708(15)00521-6</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">520</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">570</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">BIODIV</subfield><subfield code="q">DE-30</subfield><subfield code="2">fid</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">44.94</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Long, Ling</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Some supercongruences occurring in truncated hypergeometric series</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016transfer abstract</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">36</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">z</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zu</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Hypergeometric series</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Supercongruences</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">p-adic Gamma functions</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Ramakrishna, Ravi</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="n">Elsevier</subfield><subfield code="a">MacKenzie, Shannon M. ELSEVIER</subfield><subfield code="t">Evidence of Titan’s climate history from evaporite distribution</subfield><subfield code="d">2014</subfield><subfield code="g">Amsterdam [u.a.]</subfield><subfield code="w">(DE-627)ELV012586625</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:290</subfield><subfield code="g">year:2016</subfield><subfield code="g">day:26</subfield><subfield code="g">month:02</subfield><subfield code="g">pages:773-808</subfield><subfield code="g">extent:36</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1016/j.aim.2015.11.043</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ELV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">FID-BIODIV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_359</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">44.94</subfield><subfield code="j">Hals-Nasen-Ohrenheilkunde</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">290</subfield><subfield code="j">2016</subfield><subfield code="b">26</subfield><subfield code="c">0226</subfield><subfield code="h">773-808</subfield><subfield code="g">36</subfield></datafield><datafield tag="953" ind1=" " ind2=" "><subfield code="2">045F</subfield><subfield code="a">510</subfield></datafield></record></collection>
|
| author |
Long, Ling |
| spellingShingle |
Long, Ling ddc 510 ddc 520 ddc 530 ddc 570 fid BIODIV bkl 44.94 Elsevier Hypergeometric series Elsevier Supercongruences Elsevier p-adic Gamma functions Some supercongruences occurring in truncated hypergeometric series |
| authorStr |
Long, Ling |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)ELV012586625 |
| format |
electronic Article |
| dewey-ones |
510 - Mathematics 520 - Astronomy & allied sciences 530 - Physics 570 - Life sciences; biology |
| delete_txt_mv |
keep |
| author_role |
aut |
| collection |
elsevier |
| remote_str |
true |
| illustrated |
Not Illustrated |
| topic_title |
510 510 DE-600 520 VZ 530 VZ 570 VZ BIODIV DE-30 fid 44.94 bkl Some supercongruences occurring in truncated hypergeometric series Hypergeometric series Elsevier Supercongruences Elsevier p-adic Gamma functions Elsevier |
| topic |
ddc 510 ddc 520 ddc 530 ddc 570 fid BIODIV bkl 44.94 Elsevier Hypergeometric series Elsevier Supercongruences Elsevier p-adic Gamma functions |
| topic_unstemmed |
ddc 510 ddc 520 ddc 530 ddc 570 fid BIODIV bkl 44.94 Elsevier Hypergeometric series Elsevier Supercongruences Elsevier p-adic Gamma functions |
| topic_browse |
ddc 510 ddc 520 ddc 530 ddc 570 fid BIODIV bkl 44.94 Elsevier Hypergeometric series Elsevier Supercongruences Elsevier p-adic Gamma functions |
| format_facet |
Elektronische Aufsätze Aufsätze Elektronische Ressource |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
zu |
| author2_variant |
r r rr |
| hierarchy_parent_title |
Evidence of Titan’s climate history from evaporite distribution |
| hierarchy_parent_id |
ELV012586625 |
| dewey-tens |
510 - Mathematics 520 - Astronomy 530 - Physics 570 - Life sciences; biology |
| hierarchy_top_title |
Evidence of Titan’s climate history from evaporite distribution |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)ELV012586625 |
| title |
Some supercongruences occurring in truncated hypergeometric series |
| ctrlnum |
(DE-627)ELV035552050 (ELSEVIER)S0001-8708(15)00521-6 |
| title_full |
Some supercongruences occurring in truncated hypergeometric series |
| author_sort |
Long, Ling |
| journal |
Evidence of Titan’s climate history from evaporite distribution |
| journalStr |
Evidence of Titan’s climate history from evaporite distribution |
| lang_code |
eng |
| isOA_bool |
false |
| dewey-hundreds |
500 - Science |
| recordtype |
marc |
| publishDateSort |
2016 |
| contenttype_str_mv |
zzz |
| container_start_page |
773 |
| author_browse |
Long, Ling |
| container_volume |
290 |
| physical |
36 |
| class |
510 510 DE-600 520 VZ 530 VZ 570 VZ BIODIV DE-30 fid 44.94 bkl |
| format_se |
Elektronische Aufsätze |
| author-letter |
Long, Ling |
| doi_str_mv |
10.1016/j.aim.2015.11.043 |
| dewey-full |
510 520 530 570 |
| title_sort |
some supercongruences occurring in truncated hypergeometric series |
| title_auth |
Some supercongruences occurring in truncated hypergeometric series |
| abstract |
For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. |
| abstractGer |
For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. |
| abstract_unstemmed |
For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. |
| collection_details |
GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA GBV_ILN_22 GBV_ILN_359 |
| title_short |
Some supercongruences occurring in truncated hypergeometric series |
| url |
https://doi.org/10.1016/j.aim.2015.11.043 |
| remote_bool |
true |
| author2 |
Ramakrishna, Ravi |
| author2Str |
Ramakrishna, Ravi |
| ppnlink |
ELV012586625 |
| mediatype_str_mv |
z |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| author2_role |
oth |
| doi_str |
10.1016/j.aim.2015.11.043 |
| up_date |
2024-07-06T17:50:45.724Z |
| _version_ |
1803852967550386176 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">ELV035552050</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230625204651.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">180603s2016 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.aim.2015.11.043</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">GBVA2016020000011.pica</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV035552050</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0001-8708(15)00521-6</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">520</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">570</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">BIODIV</subfield><subfield code="q">DE-30</subfield><subfield code="2">fid</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">44.94</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Long, Ling</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Some supercongruences occurring in truncated hypergeometric series</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016transfer abstract</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">36</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">z</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zu</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Hypergeometric series</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Supercongruences</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">p-adic Gamma functions</subfield><subfield code="2">Elsevier</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Ramakrishna, Ravi</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="n">Elsevier</subfield><subfield code="a">MacKenzie, Shannon M. ELSEVIER</subfield><subfield code="t">Evidence of Titan’s climate history from evaporite distribution</subfield><subfield code="d">2014</subfield><subfield code="g">Amsterdam [u.a.]</subfield><subfield code="w">(DE-627)ELV012586625</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:290</subfield><subfield code="g">year:2016</subfield><subfield code="g">day:26</subfield><subfield code="g">month:02</subfield><subfield code="g">pages:773-808</subfield><subfield code="g">extent:36</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1016/j.aim.2015.11.043</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ELV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">FID-BIODIV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_359</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">44.94</subfield><subfield code="j">Hals-Nasen-Ohrenheilkunde</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">290</subfield><subfield code="j">2016</subfield><subfield code="b">26</subfield><subfield code="c">0226</subfield><subfield code="h">773-808</subfield><subfield code="g">36</subfield></datafield><datafield tag="953" ind1=" " ind2=" "><subfield code="2">045F</subfield><subfield code="a">510</subfield></datafield></record></collection>
|
| score |
7.400114 |