Gaussian test functions and Jacquet-Rallis transfer
Representation Theory
2025-08-19 v1 Number Theory
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.
Keywords
Cite
@article{arxiv.2508.12598,
title = {Gaussian test functions and Jacquet-Rallis transfer},
author = {Andreas Mihatsch and Siddarth Sankaran and Tonghai Yang},
journal= {arXiv preprint arXiv:2508.12598},
year = {2025}
}
Comments
27 pages, comments are welcome