Triple product L-functions: first reduction

Abstract: I will describe a period integral that unfolds to the triple product L-function times L-functions whose analytic properties are understood.  Motivated by the period integral, I will then formulate an extension of the Poisson summation conjecture of  Braverman-Kazhdan, L. Lafforgue, Ngo, and Sakellaridis that implies the expected analytic properties of triple product L-functions. Time permitting, I will explain how to reduce this case of the Poisson summation conjecture to a simpler case in which spectral methods can be employed together with certain local compatibility statements.  This is joint work with P. Gu, C-H. Hsu, and S. Leslie.

algebraic geometrynumber theory

Audience: researchers in the topic

Luxembourg Number Theory Day 2024