q-supercongruences from Watson's 8φ7 transformation-Reference-Cited by-同舟云学术

q-supercongruences from Watson's ₈φ₇ transformation

Published:2024-02-20 Issue: Volume: Page:
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Wang Xiaoxia¹,Xu Chang²

Affiliation:

1. Department of Mathematics , [ 34747]Shanghai University; and Newtouch Center for Mathematics of Shanghai University , Shanghai , 200444 , P. R. China

2. School of Mathematical Sciences , [ 12655]East China Normal University, Shanghai 200241 , P. R. China

Abstract

Abstract Employing Watson’s ϕ 7 8

{{}_{8}\phi_{7}}

transformation formula, we unearth several q-supercongruences with a parameter s. Particularly, one of our results is an extension of a q-analogue of Van Hamme’s (G.2) supercongruence. In addition, we obtain a q-supercongruence modulo the fifth power of a cyclotomic polynomial and propose two related conjectures.

Funder

National Natural Science Foundation of China

Natural Science Foundation of Shanghai

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/forum-2023-0409/pdf

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3. G. Gasper and M. Rahman, Basic Hypergeometric Series, 2nd ed., Encyclopedia Math. Appl. 96, Cambridge University, Cambridge, 2004.

4. V. J. W. Guo and X. Lian, A new q-analogue of Van Hamme’s (G.2) supercongruence for primes p ≡ 3 ( mod 4 ) p\equiv 3\pmod{4} , Bull. Korean Math. Soc. 60 (2023), no. 3, 775–783.

5. V. J. W. Guo and M. J. Schlosser, A family of q-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial, Israel J. Math. 240 (2020), no. 2, 821–835.

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