Distribution of Satake
parameters of GL2 holomorphic cuspidal representations
Dr. Charles, Chun Che LI
Academia Sinica, Institute of
Abstract
We prove that for a fixed non-archimedean
place v of a totally real number
field F, the traces of the associated
Langlands' conjugacy
classes of holomorphic cuspidal
representations of GL2(AF) of prime levels is equidistributed with respect to the measure
where qv is the norm of v and is the Sato-Tate
measure. This generalizes a result of Serre on the
distribution of Hecke eigenvalues
of modular forms. The proof involves establishing a trace formula for the Hecke operators. While not explicit, this trace formula can
be used as a starting point for generalizing the Eichler-Selberg
trace formula to totally real number fields.
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Room 517, Meng Wah Complex, HKU |
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All are
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