论文标题
$ q $ -supercongrences modulo循环多项式的第四强度
Some $q$-supercongruences modulo the fourth power of a cyclotomic polynomial
论文作者
论文摘要
就Guo和Zudilin最近引入的创意显微镜方法以及中国剩余定理的Cocrime多项式定理，我们建立了一个$ Q $ -Supercongruence，其中有两个参数模元$ [n]φ_n（q）^3 $。这里$ [n] =（1-q^n）/（1-q）$和$φ_n（q）$是$ n $ th cyclotomic多项式中的$ q $。特别是，我们确认了最近对郭的猜想，并给出了朗的超级努力的完整$ q $ analogue。后者也是对Guo and Schlosser获得的最近$ Q $ supercongruence的概括。
In terms of the creative microscoping method recently introduced by Guo and Zudilin and the Chinese remainder theorem for coprime polynomials, we establish a $q$-supercongruence with two parameters modulo $[n]Φ_n(q)^3$. Here $[n]=(1-q^n)/(1-q)$ and $Φ_n(q)$ is the $n$-th cyclotomic polynomial in $q$. In particular, we confirm a recent conjecture of Guo and give a complete $q$-analogue of Long's supercongruence. The latter is also a generalization of a recent $q$-supercongruence obtained by Guo and Schlosser.
