Frobenius structure on hypergeometric equations, p-adic polygamma values and p-adic L-values
Abstract
Recently, Kedlaya proves certain formula describing explicitly the Frobenius structure on a hypergeometric equation. In this paper, we give a generalization of it. In our case, the Frobenius matrix is no longer described by p-adic gamma function, and then we describe it by the p-adic polygamma functions. Since the p-adic polygamma values are linear combinations of p-adic L-values of Dirichlet characters, it turns out that the Frobenius matrix is described by p-adic L-values. Our result has an application to the study on Frobenius on p-adic cohomology. We show that, for a projective smooth family such that the Picard-Fuchs equation is a hypergeometric equation, the Frobenius matrix on the log-crystalline cohomology is described by some values of the logarithmic function and p-adic L-functions of Dirichlet characters.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
advanced mathematical theories
Advanced Algebra and Geometry
Publication details
- Journal / source
- Tunisian Journal of Mathematics
- Publisher
- Mathematical Sciences Publishers
- Volume
- 8
- Issue
- 3
- Pages
- 453–496
- Publication date
- 6 May 2026
- Language
- EN