Time: 09h15, Friday, April 08, 2022

Abstract: Automorphic L-functions introduced by Langlands in the late 60' are expected to satisfy a functional equation similar to the functional equation of Riemann's zeta function. The functional equation would follow from the Langlands' functoriality conjecture, which is one of the far-reaching goals of the Langlands program, and in a sense is equivalent to it. Around 2000, Braverman and Kazhdan formulated a new approach to the functional equation not following the route of functoriality but attempting to generalize the Fourier analysis on adeles used by Tate to prove the functional equation of the Riemann zeta function. I will report some recent progress in this approach.

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