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THE QUANTITATIVE DISTRIBUTION OF HECKE EIGENVALUES

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  10 April 2014

YINGNAN WANG
YINGNAN WANG*
Affiliation:
College of Mathematics and Computational Science, Shenzhen University, Shenzhen, Guangdong 518060, PR China email ynwang@connect.hku.hk
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Abstract

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In this paper, we prove that the Sato–Tate conjecture for primitive Maass forms holds on average. We also investigate the rate of convergence in the Sato–Tate conjecture and establish some estimates of the discrepancy with respect to the Sato–Tate measure on the average of primitive Maass forms.

Keywords

Sato–Tate conjectureMaass formsHecke eigenvaluesquantitative distribution

MSC classification

Secondary: 11F25: Hecke-Petersson operators, differential operators (one variable) 11F30: Fourier coefficients of automorphic forms
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 1 , August 2014 , pp. 28 - 36
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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