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A $q$-ANALOGUE OF A DWORK-TYPE SUPERCONGRUENCE

Part of: Discontinuous groups and automorphic forms Elementary number theory Basic hypergeometric functions

Published online by Cambridge University Press:  17 July 2020

XIAOXIA WANG Open the ORCID record for XIAOXIA WANG [Opens in a new window]  and
MINGBING YUE
XIAOXIA WANG
Affiliation:
Department of Mathematics,Shanghai University, Shanghai200444, PR China email xiaoxiawang@shu.edu.cn
MINGBING YUE*
Affiliation:
Department of Mathematics,Shanghai University, Shanghai200444, PR China email ymb17@shu.edu.cn
*
✉ymb17@shu.edu.cn
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Abstract

By making use of the ‘creative microscoping’ method, Guo and Zudilin [‘Dwork-type supercongruences through a creative $q$-microscope’, Preprint, 2020, arXiv:2001.02311] proved several Dwork-type supercongruences, including some conjectures of Swisher. In this paper, we apply the Guo–Zudilin method to prove a new Dwork-type supercongruence, which uniformly generalises several conjectures of Swisher.

Keywords

basic hypergeometric seriesq-congruencecreative microscopingcyclotomic polynomial

MSC classification

Primary: 33D15: Basic hypergeometric functions in one variable, $_rphi_s$
Secondary: 11A07: Congruences; primitive roots; residue systems 11F33: Congruences for modular and $p$-adic modular forms
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 2 , April 2021 , pp. 303 - 310
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

This work is supported by the National Natural Science Foundation of China (11661032).

References

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