论文标题
“不同的” Ramanujan型$ Q $ -Supercongrence的一些变体
Some variations of a "divergent" Ramanujan-type $q$-supercongruence
论文作者
论文摘要
使用$ Q $ -WILF - ZEILBERGER方法和$ Q $ -Analogue的“ Divergent” Ramanujan型超企业，我们给出了几个$ Q $ Q $ -Supercongruences Modulo Modulo，这是环形多项式的第四强度。其中之一是王最近证明的超级努力的$ q $ - 动物：对于任何Prime $ P> 3 $，$$，$ sum_ {k = 0}^{p-1}^{p-1}（3K-1）\ frac {（\ frac {1} {1} {2} {2} {2} {2} {2} {2} } {k！^3} 4^k \ equiv p-2p^3 \ pmod {p^4}，$$其中$（a）_k = a（a+1）\ cdots（a+k-1）$是pochhammer符号。
Using the $q$-Wilf--Zeilberger method and a $q$-analogue of a "divergent" Ramanujan-type supercongruence, we give several $q$-supercongruences modulo the fourth power of a cyclotomic polynomial. One of them is a $q$-analogue of a supercongruence recently proved by Wang: for any prime $p>3$, $$ \sum_{k=0}^{p-1} (3k-1)\frac{(\frac{1}{2})_k (-\frac{1}{2})_k^2 }{k!^3}4^k\equiv p-2p^3 \pmod{p^4}, $$ where $(a)_k=a(a+1)\cdots (a+k-1)$ is the Pochhammer symbol.
