Tian An Wong : Prehomogeneous vector spaces and the Arthur-Selberg trace formula

Posted by Frederick Saia , part of the Number Theory Seminar.

At

Sept. 26, 2025, noon

In

636 SEO

Abstract

In 2000, Langlands proposed a method to weight the Arthur-Selberg trace formula with automorphic L-functions, whose analytic behaviour is expected to detect when an automorphic form is a functorial transfer from a smaller group. An immediate obstruction that arises is the presence of nontempered representations, i.e., representations that do not satisfy the Ramanujan conjecture. It was later proposed in 2010 that an appropriate Poisson summation might be used to remove the contribution of such representations. So far, this has been carried out successfully in limited cases involving GL(2). In this talk I will introduce a general method for GL(2) and its connection to prehomogeneous vector spaces. Time permitting, I will also discuss potential consequences for the analytic behaviour of GL(2) L-functions.