International Seminar on Automorphic Forms

Andreas Mihatsch (Zhejiang University)

Construction of Gaussian test functions

The relative trace formula comparison of Jacquet–Rallis relates two trace formulas: one for general linear groups and one for unitary groups. In this context, one considers the transfer of test functions between the two sides. At the archimedean place, the Gaussian for the positive definite unitary group provides a distinguished test function that often comes up in arithmetic settings. Accordingly, it is of interest to understand its transfers to the general linear side. In my talk, I will explain a direct construction of such transfers which is based on Kudla–Millson theory. This is joint work with Siddarth Sankaran and Tonghai Yang.

https://tu-darmstadt.zoom.us/j/68048280736

The password is the first Fourier coefficient of the modular j-function (as digits)