Gaussian test functions and Jacquet-Rallis transfer

TL;DR

This paper constructs Gaussian test functions for the Jacquet-Rallis relative trace formula, enabling transfer to compact unitary groups using geometric and harmonic analysis techniques.

Contribution

It introduces explicit Gaussian test functions for the general linear group side, utilizing Kudla-Millson formalism and symmetric space properties.

Findings

Explicit transfer formulas derived

Gaussian functions constructed via geometric methods

Application to trace formula comparisons

Abstract

We construct Gaussian test functions for the general linear side of the Jacquet-Rallis relative trace formula comparison. These are functions which are defined in terms of their orbital integrals and transfer to the compact unitary group. Our construction relies on the formalism of Kudla-Millson and simple geometric properties of symmetric spaces. In particular, it also provides an explicit formula in terms of the Howe operator.