论文标题
使用wz方法的（f.3）的超级企业猜想的证明
Proof of a supercongruence conjecture of (F.3) of Swisher using the WZ-method
论文作者
论文摘要
对于非阴性整数$ m $，令$ s（m）$表示由$$ s（m）给出的总和：= \ sum_ {n = 0}^{m}^{m} \ frac {（ - 1）^n（8n+1）} {n！^3} {n！ Wz-method，对于Prime $ P \ Equiv 3 $（$ mod $ 4）$和一个奇数整数$ r> 1 $，我们在这里推论$ s \ left的超企业关系（\ frac {p^r-3} {p^r-3} {4} {4} \ right）$ n.po $ p $ -Adadic Gamma funcorm的值。结果，我们证明了Swisher提出的（F.3）的超级概念之一。这是证明$ \ frac {p^r-（d-1）} {d} $当$ p^r \ equiv -1 $ $ $（$ mod $ d）$的总和的第一次尝试。
For a non-negative integer $m$, let $S(m)$ denote the sum given by $$S(m):=\sum_{n=0}^{m}\frac{(-1)^n(8n+1)}{n!^3}\left(\frac{1}{4}\right)_n^3.$$ Using the powerful WZ-method, for a prime $p\equiv 3$ $($mod $4)$ and an odd integer $r>1$, we here deduce a supercongruence relation for $S\left(\frac{p^r-3}{4}\right)$ in terms of values of $p$-adic gamma function. As a consequence, we prove one of the supercongruence conjectures of (F.3) posed by Swisher. This is the first attempt to prove supercongruences for a sum truncated at $\frac{p^r-(d-1)}{d}$ when $p^r\equiv -1$ $($mod $d)$.
