A $q$-Dwork-type generalization of Rodriguez-Villegas' supercongruences

Abstract

Guo and Zudilin [Adv. Math. 346 (2019), 329--358] developed an analytical method, called `creative microscoping', to prove many supercongruences by establishing their $q$-analogues. In this paper, we apply this method to give a $q$-Dwork-type generalization of Rodriguez-Villegas' supercongruences, which was recently conjectured by Guo and Zudilin.