Some q-Supercongruences from a Quadratic Transformation by Rahman

Inspired by the recent work on q -congruences and a quadratic transformation formula of Rahman, we provide some new q -supercongruences. By taking parameters specialization in one of our results, we obtain a new Ramanujan-type supercongruence, which has the same right-hand side as Van Hamme’s (G.2)...

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Bibliographic Details
Published in:Resultate der Mathematik Vol. 77; no. 1
Main Authors: Liu, Yudong, Wang, Xiaoxia
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.02.2022
Subjects:
Mathematics
Mathematics and Statistics
Primary 33D15
supercongruences
cyclotomic polynomial
11B65
Basic hypergeometric series
congruences
Secondary 11A07
Rahman’s transformation formula
ISSN:1422-6383, 1420-9012
Online Access:Get full text
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Summary:Inspired by the recent work on q -congruences and a quadratic transformation formula of Rahman, we provide some new q -supercongruences. By taking parameters specialization in one of our results, we obtain a new Ramanujan-type supercongruence, which has the same right-hand side as Van Hamme’s (G.2) supercongruence for p ≡ 1 ( mod 4 ) . We also formulate some related challenging conjectures on supercongruences and q -supercongruences.
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-021-01563-7