New $ q $-supercongruences arising from a summation of basic hypergeometric series

Abstract

<abstract><p>With the help of a summation of basic hypergeometric series, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials, we prove some new $ q $-supercongruences on sums of $ q $-shifted factorials. Especially, we give a $ q $-analogue of a formula due to Liu <sup>[<xref ref-type="bibr" rid="b14">14</xref>]</sup>.</p></abstract>