Local L-values and geometric harmonic analysis on spherical varieties

Abstract: Almost a decade ago, Sakellaridis conjectured a vast generalization of the Rankin-Selberg method to produce integral representations of L-functions using affine spherical varieties. The conjecture is still very much unknown, but generalized Ichino-Ikeda formulas of Sakellaridis-Venkatesh relate the global problem to certain problems in local harmonic analysis. I will explain how we can use techniques from geometric Langlands to compute integrals which give special values of unramified local L-functions over a local function field, for a large class of spherical varieties. This is joint work with Yiannis Sakellaridis. Our results give new integral representations of L-functions (in a right half plane)​ over global function fields when the integral "unfolds".

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Columbia Automorphic Forms and Arithmetic Seminar