Transcendence of infinite series over lattices
Abstract In this paper, we study the arithmetic nature of series of the form ∑ω∈ΛA(ω)B(ω),$$\begin{aligned} \sum _{\omega \in \Lambda } \frac{A(\omega )}{B(\omega )}, \end{aligned}$$where $$\Lambda $$ is a two-dimensional lattice in $${\mathbb {C}}$$, A(X) and B(X) are suitable polynomials over $${\...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Pathak, Siddhi S. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 |
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| Übergeordnetes Werk: |
Enthalten in: The Ramanujan journal - Springer US, 1997, 56(2021), 3 vom: 19. Apr., Seite 971-992 |
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| Übergeordnetes Werk: |
volume:56 ; year:2021 ; number:3 ; day:19 ; month:04 ; pages:971-992 |
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| DOI / URN: |
10.1007/s11139-021-00420-z |
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10.1007/s11139-021-00420-z doi (DE-627)OLC2077464690 (DE-He213)s11139-021-00420-z-p DE-627 ger DE-627 rakwb eng 510 VZ 7,24 ssgn Pathak, Siddhi S. verfasserin (orcid)0000-0003-3123-4013 aut Transcendence of infinite series over lattices 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract In this paper, we study the arithmetic nature of series of the form ∑ω∈ΛA(ω)B(ω),$$\begin{aligned} \sum _{\omega \in \Lambda } \frac{A(\omega )}{B(\omega )}, \end{aligned}$$where $$\Lambda $$ is a two-dimensional lattice in $${\mathbb {C}}$$, A(X) and B(X) are suitable polynomials over $${\mathbb {C}}$$, with $$\deg A$$$$\le $$$$\deg B - 3$$. In particular, we focus on the cases when the roots of the polynomial B(X) are either algebraic numbers or rational multiples of a non-zero period of $$\Lambda $$. Elliptic functions Transcendence of infinite series Lattice sums Enthalten in The Ramanujan journal Springer US, 1997 56(2021), 3 vom: 19. Apr., Seite 971-992 (DE-627)234141301 (DE-600)1394097-1 (DE-576)100004989 1382-4090 nnns volume:56 year:2021 number:3 day:19 month:04 pages:971-992 https://doi.org/10.1007/s11139-021-00420-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT SSG-OPC-ANG AR 56 2021 3 19 04 971-992 |
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10.1007/s11139-021-00420-z doi (DE-627)OLC2077464690 (DE-He213)s11139-021-00420-z-p DE-627 ger DE-627 rakwb eng 510 VZ 7,24 ssgn Pathak, Siddhi S. verfasserin (orcid)0000-0003-3123-4013 aut Transcendence of infinite series over lattices 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract In this paper, we study the arithmetic nature of series of the form ∑ω∈ΛA(ω)B(ω),$$\begin{aligned} \sum _{\omega \in \Lambda } \frac{A(\omega )}{B(\omega )}, \end{aligned}$$where $$\Lambda $$ is a two-dimensional lattice in $${\mathbb {C}}$$, A(X) and B(X) are suitable polynomials over $${\mathbb {C}}$$, with $$\deg A$$$$\le $$$$\deg B - 3$$. In particular, we focus on the cases when the roots of the polynomial B(X) are either algebraic numbers or rational multiples of a non-zero period of $$\Lambda $$. Elliptic functions Transcendence of infinite series Lattice sums Enthalten in The Ramanujan journal Springer US, 1997 56(2021), 3 vom: 19. Apr., Seite 971-992 (DE-627)234141301 (DE-600)1394097-1 (DE-576)100004989 1382-4090 nnns volume:56 year:2021 number:3 day:19 month:04 pages:971-992 https://doi.org/10.1007/s11139-021-00420-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT SSG-OPC-ANG AR 56 2021 3 19 04 971-992 |
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10.1007/s11139-021-00420-z doi (DE-627)OLC2077464690 (DE-He213)s11139-021-00420-z-p DE-627 ger DE-627 rakwb eng 510 VZ 7,24 ssgn Pathak, Siddhi S. verfasserin (orcid)0000-0003-3123-4013 aut Transcendence of infinite series over lattices 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract In this paper, we study the arithmetic nature of series of the form ∑ω∈ΛA(ω)B(ω),$$\begin{aligned} \sum _{\omega \in \Lambda } \frac{A(\omega )}{B(\omega )}, \end{aligned}$$where $$\Lambda $$ is a two-dimensional lattice in $${\mathbb {C}}$$, A(X) and B(X) are suitable polynomials over $${\mathbb {C}}$$, with $$\deg A$$$$\le $$$$\deg B - 3$$. In particular, we focus on the cases when the roots of the polynomial B(X) are either algebraic numbers or rational multiples of a non-zero period of $$\Lambda $$. Elliptic functions Transcendence of infinite series Lattice sums Enthalten in The Ramanujan journal Springer US, 1997 56(2021), 3 vom: 19. Apr., Seite 971-992 (DE-627)234141301 (DE-600)1394097-1 (DE-576)100004989 1382-4090 nnns volume:56 year:2021 number:3 day:19 month:04 pages:971-992 https://doi.org/10.1007/s11139-021-00420-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT SSG-OPC-ANG AR 56 2021 3 19 04 971-992 |
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Abstract In this paper, we study the arithmetic nature of series of the form ∑ω∈ΛA(ω)B(ω),$$\begin{aligned} \sum _{\omega \in \Lambda } \frac{A(\omega )}{B(\omega )}, \end{aligned}$$where $$\Lambda $$ is a two-dimensional lattice in $${\mathbb {C}}$$, A(X) and B(X) are suitable polynomials over $${\mathbb {C}}$$, with $$\deg A$$$$\le $$$$\deg B - 3$$. In particular, we focus on the cases when the roots of the polynomial B(X) are either algebraic numbers or rational multiples of a non-zero period of $$\Lambda $$. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 |
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Abstract In this paper, we study the arithmetic nature of series of the form ∑ω∈ΛA(ω)B(ω),$$\begin{aligned} \sum _{\omega \in \Lambda } \frac{A(\omega )}{B(\omega )}, \end{aligned}$$where $$\Lambda $$ is a two-dimensional lattice in $${\mathbb {C}}$$, A(X) and B(X) are suitable polynomials over $${\mathbb {C}}$$, with $$\deg A$$$$\le $$$$\deg B - 3$$. In particular, we focus on the cases when the roots of the polynomial B(X) are either algebraic numbers or rational multiples of a non-zero period of $$\Lambda $$. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 |
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Abstract In this paper, we study the arithmetic nature of series of the form ∑ω∈ΛA(ω)B(ω),$$\begin{aligned} \sum _{\omega \in \Lambda } \frac{A(\omega )}{B(\omega )}, \end{aligned}$$where $$\Lambda $$ is a two-dimensional lattice in $${\mathbb {C}}$$, A(X) and B(X) are suitable polynomials over $${\mathbb {C}}$$, with $$\deg A$$$$\le $$$$\deg B - 3$$. In particular, we focus on the cases when the roots of the polynomial B(X) are either algebraic numbers or rational multiples of a non-zero period of $$\Lambda $$. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2077464690</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230505150358.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">221220s2021 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11139-021-00420-z</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2077464690</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s11139-021-00420-z-p</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="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">7,24</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Pathak, Siddhi S.</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0003-3123-4013</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Transcendence of infinite series over lattices</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, we study the arithmetic nature of series of the form ∑ω∈ΛA(ω)B(ω),$$\begin{aligned} \sum _{\omega \in \Lambda } \frac{A(\omega )}{B(\omega )}, \end{aligned}$$where $$\Lambda $$ is a two-dimensional lattice in $${\mathbb {C}}$$, A(X) and B(X) are suitable polynomials over $${\mathbb {C}}$$, with $$\deg A$$$$\le $$$$\deg B - 3$$. 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