Isolation of the Cuspidal Spectrum: the Function Field Case
Abstract
Isolating cuspidal automorphic representations from the whole automorphic spectrum is a basic problem in the trace formula approach. For example, matrix coefficients of supercupidal representations can be used as test functions for this, which kills the continuous spectrum, but also a large class of cuspidal automorphic representations. For the case of number fields, multipliers of the Schwartz algebra is used in the recent work [3] to isolate all cuspidal spectrum which provide enough test functions and suitable for the comparison of orbital integrals. These multipliers are then applied to the proof of the Gan-Gross-Prasad conjecture for unitary groups [3,2]. In this article, we prove similar result on isolating the cuspidal spectrum in [3] for the function field case.
Cite
@article{arxiv.2104.09825,
title = {Isolation of the Cuspidal Spectrum: the Function Field Case},
author = {Li Cai and Bin Xu},
journal= {arXiv preprint arXiv:2104.09825},
year = {2021}
}
Comments
The paper has been accepted for publication in SCIENCE CHINA Mathematics. A gap in the previous version is fixed