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arXiv · 1707.06091

A refined Poisson summation formula for certain Braverman-Kazhdan spaces

Jayce R. Getz·Baiying Liu
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Abstract

Braverman and Kazhdan introduced influential conjectures generalizing the Fourier transform and the Poisson summation formula. Their conjectures should imply that quite general Langlands $L$-functions have meromorphic continuations and functional equations as predicted by Langlands' functoriality conjecture. As evidence for their conjectures, Braverman and Kazhdan considered a setting related to the so-called doubling method in a later paper and proved the corresponding Poisson summation formula under restrictive assumptions on the functions involved. In this paper we consider a special case of the setting of the later paper, and prove a refined Poisson summation formula that eliminates the restrictive assumptions of loc. cit. Along the way we provide analytic control on the Schwartz space we construct; this analytic control was conjectured to hold (in a slightly different setting) in the work of Braverman and Kazhdan.

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Jayce R. Getz, Baiying Liu. 2017-11-07. A refined Poisson summation formula for certain Braverman-Kazhdan spaces. https://arxiv.org/abs/1707.06091

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