Two q-supercongruences from Watson's transformation

被引：12

作者：

Ni, He-Xia ^{[1
]}

Wang, Li-Yuan ^{[2
]}

机构：

[1] Nanjing Audit Univ, Dept Appl Math, Nanjing 211815, Peoples R China

[2] Nanjing Tech Univ, Sch Phys & Math Sci, Nanjing 211816, Peoples R China

来源：

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2022年 / 116卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Congruence; Cyclotomic polynomial; q-Binomial coefficient; Watson's transformation; SUMS;

D O I：

10.1007/s13398-021-01172-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Guo and Zudilin (Adv Math, 346: 329-358, 2019) introduced a new method called `creative microscoping', to prove many q-supercongruences in a unified way. In this paper, we apply this method and Watson's 8 phi 7 transformation formula to prove two q-supercongruences, which were recently conjectured by Guo and Schlosser.

引用

页数：7

共 40 条

[21] Some q-supercongruences modulo the square and cube of a cyclotomic polynomial
Victor J. W. Guo
Michael J. Schlosser
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2021, 115
[22] Some q-supercongruences modulo the square and cube of a cyclotomic polynomial
Guo, Victor J. W.
Schlosser, Michael J.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2021, 115 (03)
[23] Some q-Supercongruences Modulo the Fifth Power of a Cyclotomic Polynomial from Squares of q-Hypergeometric Series
Hanfei Song
Chun Wang
Results in Mathematics, 2021, 76
[24] Some q-supercongruences for truncated forms of squares of basic hypergeometric series
Li, Long
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2021, 27 (01) : 16 - 25
[25] Three families of q-supercongruences modulo the square and cube of a cyclotomic polynomial
Victor J. W. Guo
Michael J. Schlosser
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2023, 117
[26] Three families of q-supercongruences modulo the square and cube of a cyclotomic polynomial
Guo, Victor J. W.
Schlosser, Michael J.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2023, 117 (01)
[27] A New Family of q-Supercongruences Modulo the Fourth Power of a Cyclotomic Polynomial
Victor J. W. Guo
Michael J. Schlosser
Results in Mathematics, 2020, 75
[28] A New Family of q-Supercongruences Modulo the Fourth Power of a Cyclotomic Polynomial
Guo, Victor J. W.
Schlosser, Michael J.
RESULTS IN MATHEMATICS, 2020, 75 (04)
[29] q-Supercongruences modulo the fourth power of a cyclotomic polynomial via creative microscoping
Guo, Victor J. W.
ADVANCES IN APPLIED MATHEMATICS, 2020, 120
[30] A Common q-Analogue of Two Supercongruences
Guo, Victor J. W.
Zudilin, Wadim
RESULTS IN MATHEMATICS, 2020, 75 (02)

← 1 2 3 4 →