Math @ Duke

Publications [#348383] of Jayce R. Getz
Papers Published
 Getz, JR; Liu, B, A refined Poisson summation formula for certain BravermanKazhdan spaces,
Science China Mathematics
(January, 2020) [doi]
(last updated on 2020/12/03)
Abstract: © 2019, Science China Press and SpringerVerlag GmbH Germany, part of Springer Nature. Braverman and Kazhdan (2000) introduced influential conjectures aimed at generalizing the Fourier transform and the Poisson summation formula. Their conjectures should imply that quite general Langlands Lfunctions have meromorphic continuations and functional equations as predicted by Langlands’ functoriality conjecture. As evidence for their conjectures, Braverman and Kazhdan (2002) considered a setting related to the socalled doubling method in a later paper and proved the corresponding Poisson summation formula under restrictive assumptions on the functions involved. The connection between the two papers is made explicit in work of Li (2018). In this paper, we consider a special case of the setting in Braverman and Kazhdan’s later paper and prove a refined Poisson summation formula that eliminates the restrictive assumptions of that paper. 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 (2002).


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