论文标题
A $ P $ - 陈的类似物和Verrill的公式，价格为$ 1/π$
A $p$-adic analogue of Chan and Verrill's formula for $1/π$
论文作者
论文摘要
我们证明了Almkvist-zudilin数量的三个超级企业，这些超级依从确认了Zudilin和Z.-H的一些猜想。太阳。 A typical example is the Ramanujan-type supercongruence: \begin{align*} \sum_{k=0}^{p-1} \frac{4k+1}{81^k}γ_k \equiv \left(\frac{-3}{p}\right) p\pmod{p^3}, \ end {align*}对应于$ 1/π$：\ begin {align*} \ sum_ {k = 0}^\ infty \ frac {4k+1} {81^k}^k}γ_k= \ frac = \ frac {3 \ sqrt}} {2 \ end {align*}这里$γ_n$是almkvist-zudilin编号。
We prove three supercongruences for sums of Almkvist-Zudilin numbers, which confirm some conjectures of Zudilin and Z.-H. Sun. A typical example is the Ramanujan-type supercongruence: \begin{align*} \sum_{k=0}^{p-1} \frac{4k+1}{81^k}γ_k \equiv \left(\frac{-3}{p}\right) p\pmod{p^3}, \end{align*} which is corresponding to Chan and Verrill's formula for $1/π$: \begin{align*} \sum_{k=0}^\infty \frac{4k+1}{81^k}γ_k = \frac{3\sqrt{3}}{2π}. \end{align*} Here $γ_n$ are the Almkvist-Zudilin numbers.
