Papers published in the English version of the journal

A New $q$-Congruence on Double Sums

H. Song^a, C. Wang<sup>b

a</sup> School of Mathematics and Statistic, Xinyang Normal University, China
^b Department of Mathematics, Shanghai Normal University, China

Abstract: By making use of Watson's $_8\phi_7$ transformation and the Chinese remainder theorem for coprime polynomials, we obtain a $q$-congruence modulo the fourth power of a cyclotomic polynomial, which leads us to a new $q$-congruence on double sums.

Keywords: $q$-congruence, supercongruence, Chinese remainder theorem, Watson's transformation, cyclotomic polynomial.

Received: 09.09.2024
Revised: 03.04.2025

Language: English

 English version: Mathematical Notes, 2025, 118:1, 173–179

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