论文标题
$ p $ - adiC超几何功能与$ p $ - adic多重聚类有关
$p$-adic hypergeometric function related with $p$-adic multiple polylogarithms
论文作者
论文摘要
本文介绍了高斯高几幅功能的$ p $ - adic类似物，该功能沿着与Dwork不同的想法构建。我们的构建基于高几何函数与KZ方程之间的关系。我们通过调查其与$ p $ adiC多重多聚体的关系来对$ p $ adiC的超几何功能进行残留的分析延长。通过进一步探索其本地行为左右$ 1 $，我们表明，高斯高几何定理的$ p $ adiC类似物可用于该功能。
This paper introduces a $p$-adic analogue of Gauss's hypergeometric function which is constructed along ideas different from Dwork's. Our construction is based on a relationship between the hypergeometric function and the KZ equation. We perform a residue-wise analytic prolongation of our $p$-adic hypergeometric function by investigating its relationship with $p$-adic multiple polylogarithms. By further exploring its local behavior around the point $1$, we show that a $p$-adic analogue of Gauss hypergeometric theorem holds for the function.
