Number Theory Seminar

August 6, 2019 @ 2:00 pm – 3:00 pm
Keller 401 (probably)

Kiran Kedlaya of the University of California, San Diego

Title: Frobenius structures on hypergeometric equations

Abstract: Hypergeometric equations are a class of ordinary differential equations with strong ties to geometry and arithmetic. In particular, each hypergeometric equation parametrizes a family of motives with associated L-functions; the minimal example of this is the Gaussian hypergeometric equation corresponding to the Legendre family of elliptic curves. We sketch an algorithm, based on work of Dwork, to compute these L-functions using the existence of p-adic analytic “Frobenius structures” on the equation. This is expected to be useful for building tables of hypergeometric L functions for the LMFDB.