Some q-supercongruences from Rahman's summation formula

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 $p\equiv 1(\mathrm{mod}4)$. We also formulate some related challenging conjectures on supercongruences and $q$-supercongruences.

12 pages