On some determinants involving Jacobi symbols

In this paper we study some conjectures on determinants with Jacobi symbol entries posed by Z.-W. Sun. For any positive integer n ≡ 3 ( mod 4 ) , we show that ( 6 , 1 ) n = [ 6 , 1 ] n = ( 3 , 2 ) n = [ 3 , 2 ] n = 0 and ( 4 , 2 ) n = ( 8 , 8 ) n = ( 3 , 3 ) n = ( 21 , 112 ) n = 0 as conjectured by...
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Autor*in:	Krachun, Dmitry [verfasserIn] Petrov, Fedor Sun, Zhi-Wei Vsemirnov, Maxim

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020transfer abstract

Schlagwörter:	secondary 15A15 11T24 primary

Übergeordnetes Werk:	Enthalten in: Polymer-supported oligoethylene glycols as heterogeneous multifunctional catalysts for nucleophilic substitution - 2013transfer abstract, Orlando, Fla. [u.a.]
Übergeordnetes Werk:	volume:64 ; year:2020 ; pages:0

Links:	Volltext

DOI / URN:	10.1016/j.ffa.2020.101672

Katalog-ID:	ELV049942301

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245	1	0	\|a On some determinants involving Jacobi symbols
264		1	\|c 2020transfer abstract
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520			\|a In this paper we study some conjectures on determinants with Jacobi symbol entries posed by Z.-W. Sun. For any positive integer n ≡ 3 ( mod 4 ) , we show that ( 6 , 1 ) n = [ 6 , 1 ] n = ( 3 , 2 ) n = [ 3 , 2 ] n = 0 and ( 4 , 2 ) n = ( 8 , 8 ) n = ( 3 , 3 ) n = ( 21 , 112 ) n = 0 as conjectured by Sun, where ( c , d ) n = \| ( i 2 + c i j + d j 2 n ) \| 1 ≤ i , j ≤ n − 1 and [ c , d ] n = \| ( i 2 + c i j + d j 2 n ) \| 0 ≤ i , j ≤ n − 1 with ( ⋅ n ) the Jacobi symbol. We also prove that ( 10 , 9 ) p = 0 for any prime p ≡ 5 ( mod 12 ) , and [ 5 , 5 ] p = 0 for any prime p ≡ 13 , 17 ( mod 20 ) , which were also conjectured by Sun. Our proofs involve character sums over finite fields.
520			\|a In this paper we study some conjectures on determinants with Jacobi symbol entries posed by Z.-W. Sun. For any positive integer n ≡ 3 ( mod 4 ) , we show that ( 6 , 1 ) n = [ 6 , 1 ] n = ( 3 , 2 ) n = [ 3 , 2 ] n = 0 and ( 4 , 2 ) n = ( 8 , 8 ) n = ( 3 , 3 ) n = ( 21 , 112 ) n = 0 as conjectured by Sun, where ( c , d ) n = \| ( i 2 + c i j + d j 2 n ) \| 1 ≤ i , j ≤ n − 1 and [ c , d ] n = \| ( i 2 + c i j + d j 2 n ) \| 0 ≤ i , j ≤ n − 1 with ( ⋅ n ) the Jacobi symbol. We also prove that ( 10 , 9 ) p = 0 for any prime p ≡ 5 ( mod 12 ) , and [ 5 , 5 ] p = 0 for any prime p ≡ 13 , 17 ( mod 20 ) , which were also conjectured by Sun. Our proofs involve character sums over finite fields.
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700	1		\|a Petrov, Fedor \|4 oth
700	1		\|a Sun, Zhi-Wei \|4 oth
700	1		\|a Vsemirnov, Maxim \|4 oth
773	0	8	\|i Enthalten in \|n Elsevier \|t Polymer-supported oligoethylene glycols as heterogeneous multifunctional catalysts for nucleophilic substitution \|d 2013transfer abstract \|g Orlando, Fla. [u.a.] \|w (DE-627)ELV026931176
773	1	8	\|g volume:64 \|g year:2020 \|g pages:0
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912			\|a GBV_USEFLAG_U
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912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_40
912			\|a GBV_ILN_72
912			\|a GBV_ILN_92
912			\|a GBV_ILN_120
912			\|a GBV_ILN_127
912			\|a GBV_ILN_148
912			\|a GBV_ILN_241
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2005
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912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2018
912			\|a GBV_ILN_2046
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2098
912			\|a GBV_ILN_2125
936	b	k	\|a 77.00 \|j Psychologie: Allgemeines \|q VZ
951			\|a AR
952			\|d 64 \|j 2020 \|h 0

Indexfelder

author_variant	d k dk
matchkey_str	krachundmitrypetrovfedorsunzhiweivsemirn:2020----:noeeemnnsnovnjc
hierarchy_sort_str	2020transfer abstract
bklnumber	77.00
publishDate	2020
allfields	10.1016/j.ffa.2020.101672 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000969.pica (DE-627)ELV049942301 (ELSEVIER)S1071-5797(20)30041-1 DE-627 ger DE-627 rakwb eng 540 VZ 610 VZ 150 VZ LING DE-30 fid 77.00 bkl Krachun, Dmitry verfasserin aut On some determinants involving Jacobi symbols 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we study some conjectures on determinants with Jacobi symbol entries posed by Z.-W. Sun. For any positive integer n ≡ 3 ( mod 4 ) , we show that ( 6 , 1 ) n = [ 6 , 1 ] n = ( 3 , 2 ) n = [ 3 , 2 ] n = 0 and ( 4 , 2 ) n = ( 8 , 8 ) n = ( 3 , 3 ) n = ( 21 , 112 ) n = 0 as conjectured by Sun, where ( c , d ) n = \| ( i 2 + c i j + d j 2 n ) \| 1 ≤ i , j ≤ n − 1 and [ c , d ] n = \| ( i 2 + c i j + d j 2 n ) \| 0 ≤ i , j ≤ n − 1 with ( ⋅ n ) the Jacobi symbol. We also prove that ( 10 , 9 ) p = 0 for any prime p ≡ 5 ( mod 12 ) , and [ 5 , 5 ] p = 0 for any prime p ≡ 13 , 17 ( mod 20 ) , which were also conjectured by Sun. Our proofs involve character sums over finite fields. In this paper we study some conjectures on determinants with Jacobi symbol entries posed by Z.-W. Sun. For any positive integer n ≡ 3 ( mod 4 ) , we show that ( 6 , 1 ) n = [ 6 , 1 ] n = ( 3 , 2 ) n = [ 3 , 2 ] n = 0 and ( 4 , 2 ) n = ( 8 , 8 ) n = ( 3 , 3 ) n = ( 21 , 112 ) n = 0 as conjectured by Sun, where ( c , d ) n = \| ( i 2 + c i j + d j 2 n ) \| 1 ≤ i , j ≤ n − 1 and [ c , d ] n = \| ( i 2 + c i j + d j 2 n ) \| 0 ≤ i , j ≤ n − 1 with ( ⋅ n ) the Jacobi symbol. We also prove that ( 10 , 9 ) p = 0 for any prime p ≡ 5 ( mod 12 ) , and [ 5 , 5 ] p = 0 for any prime p ≡ 13 , 17 ( mod 20 ) , which were also conjectured by Sun. Our proofs involve character sums over finite fields. secondary Elsevier 15A15 Elsevier 11T24 Elsevier primary Elsevier Petrov, Fedor oth Sun, Zhi-Wei oth Vsemirnov, Maxim oth Enthalten in Elsevier Polymer-supported oligoethylene glycols as heterogeneous multifunctional catalysts for nucleophilic substitution 2013transfer abstract Orlando, Fla. [u.a.] (DE-627)ELV026931176 volume:64 year:2020 pages:0 https://doi.org/10.1016/j.ffa.2020.101672 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-LING GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_40 GBV_ILN_72 GBV_ILN_92 GBV_ILN_120 GBV_ILN_127 GBV_ILN_148 GBV_ILN_241 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2018 GBV_ILN_2046 GBV_ILN_2048 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2098 GBV_ILN_2125 77.00 Psychologie: Allgemeines VZ AR 64 2020 0
spelling	10.1016/j.ffa.2020.101672 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000969.pica (DE-627)ELV049942301 (ELSEVIER)S1071-5797(20)30041-1 DE-627 ger DE-627 rakwb eng 540 VZ 610 VZ 150 VZ LING DE-30 fid 77.00 bkl Krachun, Dmitry verfasserin aut On some determinants involving Jacobi symbols 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we study some conjectures on determinants with Jacobi symbol entries posed by Z.-W. Sun. For any positive integer n ≡ 3 ( mod 4 ) , we show that ( 6 , 1 ) n = [ 6 , 1 ] n = ( 3 , 2 ) n = [ 3 , 2 ] n = 0 and ( 4 , 2 ) n = ( 8 , 8 ) n = ( 3 , 3 ) n = ( 21 , 112 ) n = 0 as conjectured by Sun, where ( c , d ) n = \| ( i 2 + c i j + d j 2 n ) \| 1 ≤ i , j ≤ n − 1 and [ c , d ] n = \| ( i 2 + c i j + d j 2 n ) \| 0 ≤ i , j ≤ n − 1 with ( ⋅ n ) the Jacobi symbol. We also prove that ( 10 , 9 ) p = 0 for any prime p ≡ 5 ( mod 12 ) , and [ 5 , 5 ] p = 0 for any prime p ≡ 13 , 17 ( mod 20 ) , which were also conjectured by Sun. Our proofs involve character sums over finite fields. In this paper we study some conjectures on determinants with Jacobi symbol entries posed by Z.-W. Sun. For any positive integer n ≡ 3 ( mod 4 ) , we show that ( 6 , 1 ) n = [ 6 , 1 ] n = ( 3 , 2 ) n = [ 3 , 2 ] n = 0 and ( 4 , 2 ) n = ( 8 , 8 ) n = ( 3 , 3 ) n = ( 21 , 112 ) n = 0 as conjectured by Sun, where ( c , d ) n = \| ( i 2 + c i j + d j 2 n ) \| 1 ≤ i , j ≤ n − 1 and [ c , d ] n = \| ( i 2 + c i j + d j 2 n ) \| 0 ≤ i , j ≤ n − 1 with ( ⋅ n ) the Jacobi symbol. We also prove that ( 10 , 9 ) p = 0 for any prime p ≡ 5 ( mod 12 ) , and [ 5 , 5 ] p = 0 for any prime p ≡ 13 , 17 ( mod 20 ) , which were also conjectured by Sun. Our proofs involve character sums over finite fields. secondary Elsevier 15A15 Elsevier 11T24 Elsevier primary Elsevier Petrov, Fedor oth Sun, Zhi-Wei oth Vsemirnov, Maxim oth Enthalten in Elsevier Polymer-supported oligoethylene glycols as heterogeneous multifunctional catalysts for nucleophilic substitution 2013transfer abstract Orlando, Fla. [u.a.] (DE-627)ELV026931176 volume:64 year:2020 pages:0 https://doi.org/10.1016/j.ffa.2020.101672 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-LING GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_40 GBV_ILN_72 GBV_ILN_92 GBV_ILN_120 GBV_ILN_127 GBV_ILN_148 GBV_ILN_241 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2018 GBV_ILN_2046 GBV_ILN_2048 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2098 GBV_ILN_2125 77.00 Psychologie: Allgemeines VZ AR 64 2020 0
allfields_unstemmed	10.1016/j.ffa.2020.101672 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000969.pica (DE-627)ELV049942301 (ELSEVIER)S1071-5797(20)30041-1 DE-627 ger DE-627 rakwb eng 540 VZ 610 VZ 150 VZ LING DE-30 fid 77.00 bkl Krachun, Dmitry verfasserin aut On some determinants involving Jacobi symbols 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we study some conjectures on determinants with Jacobi symbol entries posed by Z.-W. Sun. For any positive integer n ≡ 3 ( mod 4 ) , we show that ( 6 , 1 ) n = [ 6 , 1 ] n = ( 3 , 2 ) n = [ 3 , 2 ] n = 0 and ( 4 , 2 ) n = ( 8 , 8 ) n = ( 3 , 3 ) n = ( 21 , 112 ) n = 0 as conjectured by Sun, where ( c , d ) n = \| ( i 2 + c i j + d j 2 n ) \| 1 ≤ i , j ≤ n − 1 and [ c , d ] n = \| ( i 2 + c i j + d j 2 n ) \| 0 ≤ i , j ≤ n − 1 with ( ⋅ n ) the Jacobi symbol. We also prove that ( 10 , 9 ) p = 0 for any prime p ≡ 5 ( mod 12 ) , and [ 5 , 5 ] p = 0 for any prime p ≡ 13 , 17 ( mod 20 ) , which were also conjectured by Sun. Our proofs involve character sums over finite fields. In this paper we study some conjectures on determinants with Jacobi symbol entries posed by Z.-W. Sun. For any positive integer n ≡ 3 ( mod 4 ) , we show that ( 6 , 1 ) n = [ 6 , 1 ] n = ( 3 , 2 ) n = [ 3 , 2 ] n = 0 and ( 4 , 2 ) n = ( 8 , 8 ) n = ( 3 , 3 ) n = ( 21 , 112 ) n = 0 as conjectured by Sun, where ( c , d ) n = \| ( i 2 + c i j + d j 2 n ) \| 1 ≤ i , j ≤ n − 1 and [ c , d ] n = \| ( i 2 + c i j + d j 2 n ) \| 0 ≤ i , j ≤ n − 1 with ( ⋅ n ) the Jacobi symbol. We also prove that ( 10 , 9 ) p = 0 for any prime p ≡ 5 ( mod 12 ) , and [ 5 , 5 ] p = 0 for any prime p ≡ 13 , 17 ( mod 20 ) , which were also conjectured by Sun. Our proofs involve character sums over finite fields. secondary Elsevier 15A15 Elsevier 11T24 Elsevier primary Elsevier Petrov, Fedor oth Sun, Zhi-Wei oth Vsemirnov, Maxim oth Enthalten in Elsevier Polymer-supported oligoethylene glycols as heterogeneous multifunctional catalysts for nucleophilic substitution 2013transfer abstract Orlando, Fla. [u.a.] (DE-627)ELV026931176 volume:64 year:2020 pages:0 https://doi.org/10.1016/j.ffa.2020.101672 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-LING GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_40 GBV_ILN_72 GBV_ILN_92 GBV_ILN_120 GBV_ILN_127 GBV_ILN_148 GBV_ILN_241 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2018 GBV_ILN_2046 GBV_ILN_2048 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2098 GBV_ILN_2125 77.00 Psychologie: Allgemeines VZ AR 64 2020 0
allfieldsGer	10.1016/j.ffa.2020.101672 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000969.pica (DE-627)ELV049942301 (ELSEVIER)S1071-5797(20)30041-1 DE-627 ger DE-627 rakwb eng 540 VZ 610 VZ 150 VZ LING DE-30 fid 77.00 bkl Krachun, Dmitry verfasserin aut On some determinants involving Jacobi symbols 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we study some conjectures on determinants with Jacobi symbol entries posed by Z.-W. Sun. For any positive integer n ≡ 3 ( mod 4 ) , we show that ( 6 , 1 ) n = [ 6 , 1 ] n = ( 3 , 2 ) n = [ 3 , 2 ] n = 0 and ( 4 , 2 ) n = ( 8 , 8 ) n = ( 3 , 3 ) n = ( 21 , 112 ) n = 0 as conjectured by Sun, where ( c , d ) n = \| ( i 2 + c i j + d j 2 n ) \| 1 ≤ i , j ≤ n − 1 and [ c , d ] n = \| ( i 2 + c i j + d j 2 n ) \| 0 ≤ i , j ≤ n − 1 with ( ⋅ n ) the Jacobi symbol. We also prove that ( 10 , 9 ) p = 0 for any prime p ≡ 5 ( mod 12 ) , and [ 5 , 5 ] p = 0 for any prime p ≡ 13 , 17 ( mod 20 ) , which were also conjectured by Sun. Our proofs involve character sums over finite fields. In this paper we study some conjectures on determinants with Jacobi symbol entries posed by Z.-W. Sun. For any positive integer n ≡ 3 ( mod 4 ) , we show that ( 6 , 1 ) n = [ 6 , 1 ] n = ( 3 , 2 ) n = [ 3 , 2 ] n = 0 and ( 4 , 2 ) n = ( 8 , 8 ) n = ( 3 , 3 ) n = ( 21 , 112 ) n = 0 as conjectured by Sun, where ( c , d ) n = \| ( i 2 + c i j + d j 2 n ) \| 1 ≤ i , j ≤ n − 1 and [ c , d ] n = \| ( i 2 + c i j + d j 2 n ) \| 0 ≤ i , j ≤ n − 1 with ( ⋅ n ) the Jacobi symbol. We also prove that ( 10 , 9 ) p = 0 for any prime p ≡ 5 ( mod 12 ) , and [ 5 , 5 ] p = 0 for any prime p ≡ 13 , 17 ( mod 20 ) , which were also conjectured by Sun. Our proofs involve character sums over finite fields. secondary Elsevier 15A15 Elsevier 11T24 Elsevier primary Elsevier Petrov, Fedor oth Sun, Zhi-Wei oth Vsemirnov, Maxim oth Enthalten in Elsevier Polymer-supported oligoethylene glycols as heterogeneous multifunctional catalysts for nucleophilic substitution 2013transfer abstract Orlando, Fla. [u.a.] (DE-627)ELV026931176 volume:64 year:2020 pages:0 https://doi.org/10.1016/j.ffa.2020.101672 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-LING GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_40 GBV_ILN_72 GBV_ILN_92 GBV_ILN_120 GBV_ILN_127 GBV_ILN_148 GBV_ILN_241 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2018 GBV_ILN_2046 GBV_ILN_2048 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2098 GBV_ILN_2125 77.00 Psychologie: Allgemeines VZ AR 64 2020 0
allfieldsSound	10.1016/j.ffa.2020.101672 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000969.pica (DE-627)ELV049942301 (ELSEVIER)S1071-5797(20)30041-1 DE-627 ger DE-627 rakwb eng 540 VZ 610 VZ 150 VZ LING DE-30 fid 77.00 bkl Krachun, Dmitry verfasserin aut On some determinants involving Jacobi symbols 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we study some conjectures on determinants with Jacobi symbol entries posed by Z.-W. Sun. For any positive integer n ≡ 3 ( mod 4 ) , we show that ( 6 , 1 ) n = [ 6 , 1 ] n = ( 3 , 2 ) n = [ 3 , 2 ] n = 0 and ( 4 , 2 ) n = ( 8 , 8 ) n = ( 3 , 3 ) n = ( 21 , 112 ) n = 0 as conjectured by Sun, where ( c , d ) n = \| ( i 2 + c i j + d j 2 n ) \| 1 ≤ i , j ≤ n − 1 and [ c , d ] n = \| ( i 2 + c i j + d j 2 n ) \| 0 ≤ i , j ≤ n − 1 with ( ⋅ n ) the Jacobi symbol. We also prove that ( 10 , 9 ) p = 0 for any prime p ≡ 5 ( mod 12 ) , and [ 5 , 5 ] p = 0 for any prime p ≡ 13 , 17 ( mod 20 ) , which were also conjectured by Sun. Our proofs involve character sums over finite fields. In this paper we study some conjectures on determinants with Jacobi symbol entries posed by Z.-W. Sun. For any positive integer n ≡ 3 ( mod 4 ) , we show that ( 6 , 1 ) n = [ 6 , 1 ] n = ( 3 , 2 ) n = [ 3 , 2 ] n = 0 and ( 4 , 2 ) n = ( 8 , 8 ) n = ( 3 , 3 ) n = ( 21 , 112 ) n = 0 as conjectured by Sun, where ( c , d ) n = \| ( i 2 + c i j + d j 2 n ) \| 1 ≤ i , j ≤ n − 1 and [ c , d ] n = \| ( i 2 + c i j + d j 2 n ) \| 0 ≤ i , j ≤ n − 1 with ( ⋅ n ) the Jacobi symbol. We also prove that ( 10 , 9 ) p = 0 for any prime p ≡ 5 ( mod 12 ) , and [ 5 , 5 ] p = 0 for any prime p ≡ 13 , 17 ( mod 20 ) , which were also conjectured by Sun. Our proofs involve character sums over finite fields. secondary Elsevier 15A15 Elsevier 11T24 Elsevier primary Elsevier Petrov, Fedor oth Sun, Zhi-Wei oth Vsemirnov, Maxim oth Enthalten in Elsevier Polymer-supported oligoethylene glycols as heterogeneous multifunctional catalysts for nucleophilic substitution 2013transfer abstract Orlando, Fla. [u.a.] (DE-627)ELV026931176 volume:64 year:2020 pages:0 https://doi.org/10.1016/j.ffa.2020.101672 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-LING GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_40 GBV_ILN_72 GBV_ILN_92 GBV_ILN_120 GBV_ILN_127 GBV_ILN_148 GBV_ILN_241 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2018 GBV_ILN_2046 GBV_ILN_2048 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2098 GBV_ILN_2125 77.00 Psychologie: Allgemeines VZ AR 64 2020 0
language	English
source	Enthalten in Polymer-supported oligoethylene glycols as heterogeneous multifunctional catalysts for nucleophilic substitution Orlando, Fla. [u.a.] volume:64 year:2020 pages:0
sourceStr	Enthalten in Polymer-supported oligoethylene glycols as heterogeneous multifunctional catalysts for nucleophilic substitution Orlando, Fla. [u.a.] volume:64 year:2020 pages:0
format_phy_str_mv	Article
bklname	Psychologie: Allgemeines
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container_title	Polymer-supported oligoethylene glycols as heterogeneous multifunctional catalysts for nucleophilic substitution
authorswithroles_txt_mv	Krachun, Dmitry @@aut@@ Petrov, Fedor @@oth@@ Sun, Zhi-Wei @@oth@@ Vsemirnov, Maxim @@oth@@
publishDateDaySort_date	2020-01-01T00:00:00Z
hierarchy_top_id	ELV026931176
dewey-sort	3540
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Sun. For any positive integer n ≡ 3 ( mod 4 ) , we show that ( 6 , 1 ) n = [ 6 , 1 ] n = ( 3 , 2 ) n = [ 3 , 2 ] n = 0 and ( 4 , 2 ) n = ( 8 , 8 ) n = ( 3 , 3 ) n = ( 21 , 112 ) n = 0 as conjectured by Sun, where ( c , d ) n = \| ( i 2 + c i j + d j 2 n ) \| 1 ≤ i , j ≤ n − 1 and [ c , d ] n = \| ( i 2 + c i j + d j 2 n ) \| 0 ≤ i , j ≤ n − 1 with ( ⋅ n ) the Jacobi symbol. We also prove that ( 10 , 9 ) p = 0 for any prime p ≡ 5 ( mod 12 ) , and [ 5 , 5 ] p = 0 for any prime p ≡ 13 , 17 ( mod 20 ) , which were also conjectured by Sun. Our proofs involve character sums over finite fields.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">In this paper we study some conjectures on determinants with Jacobi symbol entries posed by Z.-W. Sun. For any positive integer n ≡ 3 ( mod 4 ) , we show that ( 6 , 1 ) n = [ 6 , 1 ] n = ( 3 , 2 ) n = [ 3 , 2 ] n = 0 and ( 4 , 2 ) n = ( 8 , 8 ) n = ( 3 , 3 ) n = ( 21 , 112 ) n = 0 as conjectured by Sun, where ( c , d ) n = \| ( i 2 + c i j + d j 2 n ) \| 1 ≤ i , j ≤ n − 1 and [ c , d ] n = \| ( i 2 + c i j + d j 2 n ) \| 0 ≤ i , j ≤ n − 1 with ( ⋅ n ) the Jacobi symbol. We also prove that ( 10 , 9 ) p = 0 for any prime p ≡ 5 ( mod 12 ) , and [ 5 , 5 ] p = 0 for any prime p ≡ 13 , 17 ( mod 20 ) , which were also conjectured by Sun. 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author	Krachun, Dmitry
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hierarchy_parent_title	Polymer-supported oligoethylene glycols as heterogeneous multifunctional catalysts for nucleophilic substitution
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title	On some determinants involving Jacobi symbols
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title_full	On some determinants involving Jacobi symbols
author_sort	Krachun, Dmitry
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title_sort	on some determinants involving jacobi symbols
title_auth	On some determinants involving Jacobi symbols
abstract	In this paper we study some conjectures on determinants with Jacobi symbol entries posed by Z.-W. Sun. For any positive integer n ≡ 3 ( mod 4 ) , we show that ( 6 , 1 ) n = [ 6 , 1 ] n = ( 3 , 2 ) n = [ 3 , 2 ] n = 0 and ( 4 , 2 ) n = ( 8 , 8 ) n = ( 3 , 3 ) n = ( 21 , 112 ) n = 0 as conjectured by Sun, where ( c , d ) n = \| ( i 2 + c i j + d j 2 n ) \| 1 ≤ i , j ≤ n − 1 and [ c , d ] n = \| ( i 2 + c i j + d j 2 n ) \| 0 ≤ i , j ≤ n − 1 with ( ⋅ n ) the Jacobi symbol. We also prove that ( 10 , 9 ) p = 0 for any prime p ≡ 5 ( mod 12 ) , and [ 5 , 5 ] p = 0 for any prime p ≡ 13 , 17 ( mod 20 ) , which were also conjectured by Sun. Our proofs involve character sums over finite fields.
abstractGer	In this paper we study some conjectures on determinants with Jacobi symbol entries posed by Z.-W. Sun. For any positive integer n ≡ 3 ( mod 4 ) , we show that ( 6 , 1 ) n = [ 6 , 1 ] n = ( 3 , 2 ) n = [ 3 , 2 ] n = 0 and ( 4 , 2 ) n = ( 8 , 8 ) n = ( 3 , 3 ) n = ( 21 , 112 ) n = 0 as conjectured by Sun, where ( c , d ) n = \| ( i 2 + c i j + d j 2 n ) \| 1 ≤ i , j ≤ n − 1 and [ c , d ] n = \| ( i 2 + c i j + d j 2 n ) \| 0 ≤ i , j ≤ n − 1 with ( ⋅ n ) the Jacobi symbol. We also prove that ( 10 , 9 ) p = 0 for any prime p ≡ 5 ( mod 12 ) , and [ 5 , 5 ] p = 0 for any prime p ≡ 13 , 17 ( mod 20 ) , which were also conjectured by Sun. Our proofs involve character sums over finite fields.
abstract_unstemmed	In this paper we study some conjectures on determinants with Jacobi symbol entries posed by Z.-W. Sun. For any positive integer n ≡ 3 ( mod 4 ) , we show that ( 6 , 1 ) n = [ 6 , 1 ] n = ( 3 , 2 ) n = [ 3 , 2 ] n = 0 and ( 4 , 2 ) n = ( 8 , 8 ) n = ( 3 , 3 ) n = ( 21 , 112 ) n = 0 as conjectured by Sun, where ( c , d ) n = \| ( i 2 + c i j + d j 2 n ) \| 1 ≤ i , j ≤ n − 1 and [ c , d ] n = \| ( i 2 + c i j + d j 2 n ) \| 0 ≤ i , j ≤ n − 1 with ( ⋅ n ) the Jacobi symbol. We also prove that ( 10 , 9 ) p = 0 for any prime p ≡ 5 ( mod 12 ) , and [ 5 , 5 ] p = 0 for any prime p ≡ 13 , 17 ( mod 20 ) , which were also conjectured by Sun. Our proofs involve character sums over finite fields.
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title_short	On some determinants involving Jacobi symbols
url	https://doi.org/10.1016/j.ffa.2020.101672
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author2	Petrov, Fedor Sun, Zhi-Wei Vsemirnov, Maxim
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up_date	2024-07-06T22:57:56.284Z
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For any positive integer n ≡ 3 ( mod 4 ) , we show that ( 6 , 1 ) n = [ 6 , 1 ] n = ( 3 , 2 ) n = [ 3 , 2 ] n = 0 and ( 4 , 2 ) n = ( 8 , 8 ) n = ( 3 , 3 ) n = ( 21 , 112 ) n = 0 as conjectured by Sun, where ( c , d ) n = \| ( i 2 + c i j + d j 2 n ) \| 1 ≤ i , j ≤ n − 1 and [ c , d ] n = \| ( i 2 + c i j + d j 2 n ) \| 0 ≤ i , j ≤ n − 1 with ( ⋅ n ) the Jacobi symbol. We also prove that ( 10 , 9 ) p = 0 for any prime p ≡ 5 ( mod 12 ) , and [ 5 , 5 ] p = 0 for any prime p ≡ 13 , 17 ( mod 20 ) , which were also conjectured by Sun. 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