Fast evaluation of some p-adic special functions

Abstract: In this talk, I will present fast algorithms for computing values of p-adic functions which are solutions of a small linear differential equation. This includes in particular exponentials, polylogarithms, hypergeometric functions and many special functions appearing in the cohomology of p-adic fibrations. As an application, building upon previous works by Asakura and Kedlaya, I will derive an algorithm for computing special values of the Dwork hypergeometric function with quasi-linear runtime with respect to the target precision. Joint work with Marc Mezzarobba, Nobuki Takayama and Tristan Vaccon.

algebraic geometrynumber theory

Audience: researchers in the topic

Leiden Algebra, Geometry, and Number Theory Seminar