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Seminar

NGM Pizza Seminar: Weyl's law for automorphic forms and Hecke operators October 03, 2014 (11:00 AM PDT - 11:45 AM PDT)
Parent Program: New Geometric Methods in Number Theory and Automorphic Forms
Location: MSRI: Simons Auditorium
Speaker(s) Jasmin Matz (Rheinische Friedrich-Wilhelms-Universit├Ąt Bonn)
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A theorem of Weyl asserts that the number of eigenvalues of the Laplacian less than X on a compact Riemann surface of dimension d is asymptotic to a constant multiple of X^{d/2}. A similar statement is true for the number of cuspidal automorphic representations with bounded infinitesimal character of G(\R)/K for G a split adjoint semisimple group and K a maximal compact subgroup of G(\R) (Selberg, Miller, Müller, Lindenstrauss-Venkatesh). Instead of just counting automorphic forms, it is also of interest to weight this counting by traces of Hecke operators. An asymptotic for this problem together with a bound on the error term has applications in the theory of families of L-functions. I want to explain the automorphic Weyl law, and some recent results for the problem involving Hecke operators in the case of GL(n).

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