论文标题
a $ q $ -supercongrunce模型循环多项式的第四强度
A $q$-supercongruence modulo the fourth power of a cyclotomic polynomial
论文作者
论文摘要
在本文中，具有两个免费参数模型的新的$ q $ - 苏格朗克式获得了环形多项式的第四次功率。我们的主要辅助工具是Watson的$ _8ϕ_7 $用于基本高几幅系列的转换公式，这是Guo和Zudilin最近引入的“创意显微镜”方法以及副本多项式的中文定理。通过在已建立的$ q $ - 苏格朗克环境中进行合适的参数替换，得出了一些涉及Bernoulli编号的不错的一致性。
In this paper, a new $q$-supercongruence with two free parameters modulo the fourth power of a cyclotomic polynomial is obtained. Our main auxiliary tools are Watson's $_8ϕ_7$ transformation formula for basic hypergeometric series, the `creative microscoping' method recently introduced by Guo and Zudilin and the Chinese remainder theorem for coprime polynomials. By taking suitable parameter substitutions in the established $q$-supercongruence, some nice congruences involving the Bernoulli numbers are derived.
