A family of q-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial

被引：0

作者：

Victor J. W. Guo

Michael J. Schlosser

机构：

[1] Huaiyin Normal University,School of Mathematics and Statistics

[2] Universität Wien Oskar-Morgenstern-Platz 1,Fakultät für Mathematik

来源：

Israel Journal of Mathematics | 2020年 / 240卷

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D O I：

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摘要：

We prove a two-parameter family of q-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial. Crucial ingredients in our proof are George Andrews’ multiseries extension of the Watson transformation, and a Karlsson—Minton-type summation for very-well-poised basic hypergeometric series due to George Gasper. The new family of q-congruences is then used to prove two conjectures posed earlier by the authors.

引用

页码：821 / 835

页数：14

共 29 条

[1] A family of q-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial
Guo, Victor J. W.
Schlosser, Michael J.
[J]. ISRAEL JOURNAL OF MATHEMATICS, 2020, 240 (02) : 821 - 835
[2] A FAMILY OF q-CONGRUENCES MODULO THE SQUARE OF A CYCLOTOMIC POLYNOMIAL
Guo, Victor J. W.
[J]. ELECTRONIC RESEARCH ARCHIVE, 2020, 28 (02): : 1031 - 1036
[3] Some q-Supercongruences Modulo the Fifth Power of a Cyclotomic Polynomial from Squares of q-Hypergeometric Series
Song, Hanfei
Wang, Chun
[J]. RESULTS IN MATHEMATICS, 2021, 76 (04)
[4] Some q-Supercongruences Modulo the Fifth Power of a Cyclotomic Polynomial from Squares of q-Hypergeometric Series
Hanfei Song
Chun Wang
[J]. Results in Mathematics, 2021, 76
[5] A New Family of q-Supercongruences Modulo the Fourth Power of a Cyclotomic Polynomial
Victor J. W. Guo
Michael J. Schlosser
[J]. Results in Mathematics, 2020, 75
[6] A New Family of q-Supercongruences Modulo the Fourth Power of a Cyclotomic Polynomial
Guo, Victor J. W.
Schlosser, Michael J.
[J]. RESULTS IN MATHEMATICS, 2020, 75 (04)
[7] Another Family of q-Congruences Modulo the Square of a Cyclotomic Polynomial
Guo, Victor J. W.
[J]. RESULTS IN MATHEMATICS, 2021, 76 (02)
[8] Another Family of q-Congruences Modulo the Square of a Cyclotomic Polynomial
Victor J. W. Guo
[J]. Results in Mathematics, 2021, 76
[9] A q-supercongruence modulo the fourth power of a cyclotomic polynomial
Wang, Xiaoxia
Xu, Chang
[J]. BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE, 2024, 67 (03): : 345 - 353
[10] A new q-supercongruence modulo the fourth power of a cyclotomic polynomial
Na Tang
[J]. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2023, 117

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