A refined Poisson summation formula for certain Braverman-Kazhdan spaces


Journal Article

© 2019, Science China Press and Springer-Verlag 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 L-functions 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 so-called 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).

Full Text

Duke Authors

Cited Authors

  • Getz, JR; Liu, B

Published Date

  • January 1, 2020

Published In

Electronic International Standard Serial Number (EISSN)

  • 1869-1862

International Standard Serial Number (ISSN)

  • 1674-7283

Digital Object Identifier (DOI)

  • 10.1007/s11425-018-1616-0

Citation Source

  • Scopus