Distribution of Hecke eigenvalues

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• Jasmin Matz (University of Copenhagen)
• Tuesday 28 January 2020, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Jessica Fintzen.

There are many difficult conjectures about automorphic representations, many of which seem to be out of reach at the moment. It has therefore become increasingly popular to study instead families of automorphic representations and their statistical properties, which allows for additional analytic techniques to be used.

In my talk I want to discuss the distribution of Hecke eigenvalues or, in other words, Satake parameters in the family of spherical unramified automorphic representations of split classical groups. We obtain an effective distribution of the Satake parameters, when we order the family according to the size of analytic conductor. This has applications to various questions in number theory, for example, low-lying zeros in families of automorphic L-functions, but also yields an effective Weyl law for the underlying locally symmetric space. This is joint work with T. Finis.

This talk is part of the Number Theory Seminar series.

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