Tate reformulated the theory of the Riemann zeta function and its functional equation as the Mellin shadow of the Fourier transform on a certain space of function on the adeles. Conjecturally, Langlands’ general automorphic L-functions and their functional equation can be interpreted in the same way following a framework due to Braverman and Kazhdan with the case of standard L-function associated with automorphic representations of GLn and the standard representation of the dual GLn being well known and due to Godement and Jacquet. This talk is based on a work in progress jointly with Zhilin Luo in which we propose an explicit conjectural construction for the kernel of the non abelian Fourier transform for G=GLn and arbitrary representation of the dual GLn.
This video is part of the Institute for Advanced Study‘s Number theory seminar.
