p-adic Generalized Hypergeometric Equations from the Viewpoint of Arithmetic D-modules

Abstract

We study the $p$-adic (generalized) hypergeometric equations by using the theory of multiplicative convolution of arithmetic $\mathcal{D}$-modules. As a result, we prove that the hypergeometric isocrystals with suitable rational parameters have a structure of overconvergent $F$-isocrystals.

33 pages; minor corrections

Cited by in corpus (2)

• Bessel $F$-isocrystals for reductive groups
• Irregular Hodge filtration of hypergeometric differential equations