Joint IAS/PU Number Theory

The Poisson summation conjecture of Braverman-Kazhdan, L. Lafforgue, Ngo, and Sakellaridis is an ambitious proposal to prove analytic properties of quite general Langlands L-functions using vast generalizations of the Poisson summation formula. In this talk, we introduce multivariable zeta integrals which unfold to Euler products representing the triple product L-functions times a product of L-functions with known analytic properties. We then formulate a generalization of the Poisson summation conjecture and show it implies the expected analytic properties of triple product L-functions. Finally, we propose a strategy, the fiber bundle method, to reduce this generalized conjecture to a case of the Poisson summation conjecture in which spectral methods can be employed together with certain local compatibility statements. This talk is based on joint work with Jayce Getz, Chun-Hsien Hsu, and Spencer Leslie.