$p$-adic generalized hypergeometric equations from the viewpoint of arithmetic $\scr{D}$-modules}$

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