Distribution of Hecke Eigenvalues for GL (n)
Simons Symposia（2016）
Abstract
The purpose of this survey is to briefly summarize and explain the results of Matz (Weyl's law for Hecke operators on GL(n) over imaginary quadratic number fields, 2013, arXiv: 1310.6525) and joint work with Templier (Sato-Tate equidistribution for the family of Hecke-Maass forms on SL(n,Z), arXiv: 1505.07285) about the asymptotic distribution of eigenvalues of Hecke operators on cusp forms for GL(n). We also to sketch some motivation and potential extensions of our results.
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Key words
Cusp Form, Trace Formula, Cuspidal Representation, Finite Index Subgroup, Principal Congruence Subgroup
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