Several Families of q-supercongruences on Multiple Sums

Abstract

In this paper, in view of El Bachraoui’s lemma, the creative microscoping method introduced by Guo and Zudilin, the Chinese remainder theorem for coprime polynomials, and Jackson’s ₆ϕ₅ summation formula, we establish several families of q-supercongruences modulo the fourth power of a cyclotomic polynomial on double, triple and quadruple sums respectively.

Keywords

basic hypergeometric series / q-supercongruences / creative microscoping / Chinese remainder theorem / 33D15 / 11A07 / 11B65

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Peking University