Irregular Hodge filtration of hypergeometric differential equations

Abstract

Fedorov and Sabbah--Yu calculated the (irregular) Hodge numbers of hypergeometric connections. In this paper, we study the irregular Hodge filtrations on hypergeometric connections defined by rational parameters, and provide a new proof of the aforementioned results. Our approach is based on a geometric interpretation of hypergeometric connections, which enables us to show that certain hypergeometric sums are everywhere ordinary on $|{\mathbb{G}}_{m,{\mathbb{F}}_p}|$ (i.e. "Frobenius Newton polygon equals to irregular Hodge polygon").

References in corpus (1)

• Hodge numbers of motives attached to Kloosterman and Airy moments