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arXiv · 2410.15627

Beyond Endoscopy: Poisson Summation Formula and Kuznetsov Trace Formula on $\mathrm{GL}_2$

Zhaolin Li
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Abstract

In the first part of this paper, we present a direct proof of a Poisson summation formula on the Whittaker space of $\mathrm{GL}_2$, 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 $L$-functions of $\mathrm{GL}_2$.

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Zhaolin Li. 2024-10-21. Beyond Endoscopy: Poisson Summation Formula and Kuznetsov Trace Formula on $\mathrm{GL}_2$. https://arxiv.org/abs/2410.15627

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