Number Theory Seminar
Tian An Wong
University of Michigan Dearborn
Prehomogeneous vector spaces and the Arthur-Selberg trace formula
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.
Friday September 26, 2025 at 12:00 PM in 636 SEO