EVENT DETAILS AND ABSTRACT

Title: Triply modular pre-trace formulas and their applications
Speaker: Raphael Steiner
Speaker Info: IAS
Brief Description:
Special Note:
Abstract:

We parametrise elements in the full Hecke algebra in a way such that the parametrisation represents a generic automorphic form. By convolving, we then arrive at pre-trace formulas which are modular in three variables. From here, various identities for higher moments may be derived. We give applications to the sup-norm and fourth-norm of holomorphic Hecke eigenforms as well as Hecke-Maass forms on S^3 and furthermore outline future work on higher moments of periods and quantum variance. This is joint work with Ilya Khayutin.