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Number Theory Seminar

Thursday, January 4, 2024
4:00pm to 5:00pm
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Linde Hall 387
On Triple Product L-functions
Miao Gu, Department of Mathematics, University of Michigan,

Conjectures of Braverman-Kazhdan, Lafforgue, Ngo and Sakellaridis suggest that every affine spherical variety admits a generalized Poisson summation formula. We refer to this conjecture as the Poisson summation conjecture. The Poisson summation conjecture implies the functional equation and meromorphic continuation for fairly general Langlands L-functions, which by the converse theorem, implies Langlands functoriality in great generality. In collaboration with Jayce Getz, Chun-Hsien Hsu and Spencer Leslie, we constructed a family of period integrals using certain spherical varieties related to Braverman-Kazhdan space, which are holomorphic multiples of the triple product L-function in a domain that nontrivially intersects the critical strip. If time permits, I'll also talk about some current progress towards the analytic properties by introducing a family of Whittaker inductions to the picture.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].