UCSD
When
2 – 3 a.m., Oct. 28, 2025
Where
Title: Arithmeticity for L-functions for Quaternionic Groups
Abstract: We discuss arithmeticity results for L-functions associated to automorphic forms on quaternionic groups. We describe a method, originating from Shimura, to attack Deligne's conjecture for critical values of L-functions. In particular, we investigate quaternionic modular forms (QMFs), which are non-holomorphic automorphic forms associated to the so-called quaternionic discrete series studied by Gross and Wallach. We describe recent work on the arithmeticity of Fourier coefficients for QMFs, as well as a notion of Maass-Shimura operators for QMFs.