Generalized hypergeometric arithmetic D-modules under a p-adic non-Liouvilleness condition

Abstract

We prove that the arithmetic $\mathscr{D}$-modules associated with the $p$-adic generalized hypergeometric differential operators, under a $p$-adic non-Liouvilleness condition on parameters, are described as an iterative multiplicative convolution of (hypergeometric arithmetic) $\mathscr{D}$-modules of rank one. As a corollary, we prove the overholonomicity of hypergeometric arithmetic $\mathscr{D}$-modules under a $p$-adic non-Liouvilleness condition.