Some q-supercongruences on double and triple sums

Abstract

In this paper, we investigate a number of q-supercongruences on double and triple sums. By means of a lemma devised by El Bachraoui and its generalization, we transform some q-supercongruences on double and triple sums into the q-supercongruences of the square and cube of truncated basic hypergeometric series. Our main tools still involve the 'creative microscoping' method introduced by Guo and Zudilin, a lemma designed by Guo and Li and the Chinese remainder theorem.