Irregular Hodge filtration of hypergeometric differential equations
Yichen Qin, Daxin Xu · Algebra & Number Theory · 2025
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 އ| m,ކ p |; i.e., "Frobenius Newton polygon equals the irregular Hodge polygon".