Frobenius structure on hypergeometric equations and p-adic polygamma functions

Abstract

We show the residue formula of the Frobenius intertwiners on hypergeometric differential equations, such as F(a_1,\ldots,a_n;1,\ldots,1;z)'s. This extends Kedlaya's result which gives the residue formula for F(a_1,\ldots,a_n;b_1,\ldots,b_n;z) with 0<b_j<1 and b_i\ne b_j. A new feature is that the p-adic polygamma function appears in our formula.Comment: 25 page