Geometry Seminar

 

Distribution of Satake parameters of GL2 holomorphic cuspidal representations

 

Dr. Charles, Chun Che LI

Academia Sinica, Institute of Mathematics, Taiwan

 

 

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

image007

where qv is the norm of v and image008 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.

 

Date:

November 10, 2006 (Friday)

Time:

4:00 – 5:00pm

Place:

Room 517, Meng Wah Complex, HKU

 

 

All are welcome