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Explore advanced research in number theory through this mathematical lecture that investigates the Poisson summation conjecture and its applications to triple product L-functions. Delve into the ambitious proposal by Braverman-Kazhdan, L. Lafforgue, Ngo, and Sakellaridis for proving analytic properties of general Langlands L-functions using generalizations of the Poisson summation formula. Learn about multivariable zeta integrals that unfold to Euler products representing triple product L-functions multiplied by products of L-functions with established analytic properties. Examine a formulation of the generalized Poisson summation conjecture and discover how it implies the expected analytic properties of triple product L-functions. Understand the proposed fiber bundle method strategy for reducing this generalized conjecture to cases where spectral methods can be employed alongside local compatibility statements. Gain insights into cutting-edge collaborative research conducted with Jayce Getz, Chun-Hsien Hsu, and Spencer Leslie that advances our understanding of L-functions and their analytic properties within the framework of the Langlands program.
