We discuss algorithms for arithmetic properties of hypergeometric functions. Most notably, we are able to compute the p-adic valuation of a hypergeometric function on any disk of radius smaller than the p-adic radius of convergence. This we use, building on work of Christol, to determine the set of prime numbers modulo which it can be reduced. Moreover, we describe an algorithm to find an annihilating polynomial of the reduction of a hypergeometric function modulo p.

翻译：本文探讨了超几何函数算术性质的算法。尤为重要的是，我们能够计算超几何函数在任意半径小于其p进收敛半径的圆盘上的p进赋值。基于Christol的研究成果，我们利用该方法确定了该函数可被约化的素数模集。此外，我们提出了一种算法，用于寻找超几何函数模p约化后的湮灭多项式。