Hankel transform and « beyond endoscopy » for the symmetric square L-function

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Date(s) - 12/06/2018
14 h 00 min - 15 h 00 min

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The Kuznetsov formula is a geometric way of studying the generic automorphic spectrum of a group. If we use appropriate non-standard test functions, we can study integrals over the automorphic spectrum weighted by L-functions. In this talk I will focus on the symmetric square L-function of GL(2). I will show that the functional equation translates to an explicit transformation (« Hankel transform ») on the space of orbital integrals of the Kuznetsov formula which, in principle, can be used to give an independent proof of the functional equation; and I will revisit the thesis of Akshay Venkatesh, showing how the image of the functorial lift from tori can be detected in the space of orbital integrals for the Kuznetsov formula.


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