Some New q-Congruences for Truncated Basic Hypergeometric Series: Even Powers
Some New q-Congruences for Truncated Basic Hypergeometric Series: Even Powers
复制标题
截断基本超几何级数的一些新 q 同余式：偶次幂
DOI：
10.1007/s00025-019-1126-4
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发表时间：
2020-03-01
影响因子：
2.2
通讯作者：
Schlosser, Michael J.
中科院分区：
文献类型：
--
作者：
Guo, Victor J. W.;Schlosser, Michael J.
我们给出了基为q的偶次幂的截断基本超几何级数的几个新的q-同余.我们的结果主要涉及模为分圆多项式的平方或立方的同余，并补充了前人关于基为q的奇次幂的截断基本超几何级数的q-同余的相应结果.我们还给出了一些相关猜想，包括模为割圆多项式的五次幂的q-同余和模大于3的7次方的截断普通超几何级数的同余.
We provide several new q-congruences for truncated basic hypergeometric series with the base being an even power of q. Our results mainly concern congruences modulo the square or the cube of a cyclotomic polynomial and complement corresponding ones of an earlier paper containing q-congruences for truncated basic hypergeometric series with the base being an odd power of q. We also give a number of related conjectures including q-congruences modulo the fifth power of a cyclotomic polynomial and a congruence for a truncated ordinary hypergeometric series modulo the seventh power of a prime greater than 3.