Beyond Endoscopy: Poisson Summation Formula and Kuznetsov Trace Formula on $\mathrm{GL}_2$
Number Theory
2025-02-26 v2
Abstract
In the first part of this paper, we present a direct proof of a Poisson summation formula on the Whittaker space of , which underlies the local Hankel transform computed by H. Jacquet. In the second part, we derive a Kuznetsov-type trace formula for incorporating non-standard test functions. This formulation reveals that the Poisson summation formula naturally yields the functional equation for the standard -functions of .
Cite
@article{arxiv.2410.15627,
title = {Beyond Endoscopy: Poisson Summation Formula and Kuznetsov Trace Formula on $\mathrm{GL}_2$},
author = {Zhaolin Li},
journal= {arXiv preprint arXiv:2410.15627},
year = {2025}
}