Beyond Endoscopy via Poisson Summation

Langlands proposed a strategy called Beyond Endoscopy to prove the principle of functoriality, which is one of the central questions of present-day mathematics. The Langlands strategy of beyond endoscopy is a two-step process in which the first step isolates the packets of cuspidal automorphic representations whose L-functions (for a representation of the dual group) have a pole at s=1. The second step compares this data for two different groups and aims to determine functorial transfers. This talk deals with the first step. Altug worked with the group GL(2) over the rationals. This project generalizes Altug's result to GL(2) over a totally real number field. In this talk, we will emphasize some interesting differences between our work and Altug's work. This work is joint with Malors Espinosa-Lara, Debanjana Kundu, and Tian An Wong.