On periods and L-functions for GL(4) x GL(2) and GU(2,2) x GL(2)
Antonio Cauchi
University College Dublin
https://sites.google.com/view/antoniocauchi/home
Date(s) : 10/12/2025 iCal
11h00 - 12h00
The study of periods of automorphic forms is a key theme in the Langlands program and has become an important tool to tackle various problems in Number Theory and Arithmetic Geometry. In recent years, the conjectures of Sakellaridis and Venkatesh (and then Ben-Zvi, Sakellaridis, and Venkatesh) has led to a deeper understanding of automorphic periods and their relation to special values of L-functions. In this talk, I present work in progress aimed at looking at certain non-spherical automorphic periods. Precisely, I will describe a new integral representation of the degree 12 « exterior square x standard’’ L-function on generic cusp forms on GU(2,2) x GL(2) (and GL(4) x GL(2)) and how it can be used to relate the non-vanishing of its central value to a certain cohomological period. I will then describe how this relates to a conjecture of Wan–Zhang on periods for the spherical pair (GL(2) times GL(2) , GL(4) x GL(2)). This is joint work with Armando Gutierrez Terradillos.
Emplacement
Saint-Charles
Catégories
