论文标题
$ q $ - 综合的家族模仿一个环形多项式的平方
A family of $q$-congruences modulo the square of a cyclotomic polynomial
论文作者
论文摘要
使用Watson的终止$ _8ϕ_7 $转换公式，我们证明了一个$ Q $ - 企业的家族Modulo是一个环形多项式的平方，最初是由作者和Zudilin提出的[J. [J.数学。肛门。应用。 475（2019），1636--646]。作为一个应用程序，我们推论了两个超级美食Modulo $ p^4 $（$ p $是一个奇怪的素数）及其$ q $ - analogues。这也部分证实了Swisher（H.3）猜想的特殊情况。
Using Watson's terminating $_8ϕ_7$ transformation formula, we prove a family of $q$-congruences modulo the square of a cyclotomic polynomial, which were originally conjectured by the author and Zudilin [J. Math. Anal. Appl. 475 (2019), 1636--646]. As an application, we deduce two supercongruences modulo $p^4$ ($p$ is an odd prime) and their $q$-analogues. This also partially confirms a special case of Swisher's (H.3) conjecture.
