Irregular Hodge filtration of hypergeometric differential equations

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 $\mathrm{\mid }{\mathbb{G}}_{m,{\mathbb{F}}_p}\mathrm{\mid }$ (i.e. “Frobenius Newton polygon equals to irregular Hodge polygon”).