### The Kuznetsov formula for GSp_4

Linfoot Number Theory Seminar

5th May 2021, 11:00 am – 12:00 pm

Fry Building, Online

The classical Kuznetsov formula is an identity relating the Fourier coefficients of certain automorphic forms on GL_2 to some arithmetic information (sum of Kloosterman sums). It has many applications in number theory, usually involving using either known information about Kloosterman sums to derive non-trivial results about the Fourier coefficients of Maass forms, or the other way around. Recently, analogous formulas were proven for other groups. In this talk, I will present a Kuznetsov formula for the group GSp_4. After recalling some basic properties of the group GSp_4, I will give an outline of the derivation following an adelic relative trace formula approach. The tools involve representation theory, the Langlands spectral decomposition, and some functional analysis over real groups.

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