Some q-supercongruences from Rahman's summation formula

Yudong Liu; Xiaoxia Wang

Some q-supercongruences from Rahman's summation formula

Combinatorics 2021-03-12 v1

Authors: Yudong Liu , Xiaoxia Wang

Abstract

Inspired by the recent work on $q$ -congruences and the quadratic summation formula of Rahman, we provide some new $q$ -supercongruences. By taking $q\to 1$ 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 $p\equiv 1 \pmod 4$ . We also formulate some related challenging conjectures on supercongruences and $q$ -supercongruences.

Keywords

q-series and q-analogues ramanujan identities and series

Cite

@article{arxiv.2103.06416,
  title  = {Some q-supercongruences from Rahman's summation formula},
  author = {Yudong Liu and Xiaoxia Wang},
  journal= {arXiv preprint arXiv:2103.06416},
  year   = {2021}
}

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12 pages

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