Philadelphia Area Number Theory Seminar

Wednesday, February 1, 2023 - 3:30pm

Liyang Yang

Princeton University

We will introduce a relative trace formula on GL(n + 1) weighted by cusp forms on GL(n) over number fields. The spectral side is an average of Rankin–Selberg L-functions for GL(n+ 1) × GL(n) over the full spectrum, and the geometric side consists of Rankin–Selberg L-functions for GL(n) × GL(n), and certain explicit meromorphic functions. The formula yields new results towards central L-values for GL(n + 1) × GL(n): the second moment evaluation, and simultaneous nonvnanish-ing in the level aspect. Further applications to the subconvexity problem will be discussed if time permits.