Number Theory Seminar
Eichler-Selberg relations in complex multiplication
Speaker: Ken Ono (University of Virginia)Date: Thursday, 08 May 2025 - 16:30Place: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Abstract:
The Eichler-Selberg trace formula expresses the trace of Hecke operators on spaces of cusp forms as weighted sums of Hurwitz-Kronecker class numbers. We extend this formula to a natural class of relations for traces of singular moduli, where one views class numbers as traces of the constant function. More generally, we consider the singular moduli for Zagier’s Hecke system of modular functions jm(τ ). Our results reprove Kaneko’s celebrated singular moduli formulas for the coefficients of the j-function. And more generally, give new Eichler-Selberg trace formulas for the Hecke operators on generic spaces of space of cusp forms. This is joint work with Yuqi Deng and Toshiki Matsusaka.
