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

Abstract

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