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A Remark on a Modular Analogue of the Sato–Tate Conjecture

Published online by Cambridge University Press:  20 November 2018

Wentang Kuo
Wentang Kuo*
Affiliation:
Department of Pure Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1 e-mail: wtkuo@math.uwaterloo.ca
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Abstract

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The original Sato–Tate Conjecture concerns the angle distribution of the eigenvalues arising from non-CM elliptic curves. In this paper, we formulate amodular analogue of the Sato–Tate Conjecture and prove that the angles arising from non-$\text{CM}$ holomorphic Hecke eigenforms with non-trivial central characters are not distributed with respect to the Sate–Tatemeasure for non-$\text{CM}$ elliptic curves. Furthermore, under a reasonable conjecture, we prove that the expected distribution is uniform.

Keywords

11F0311F25L-functionsElliptic curvesSato–Tate
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 50 , Issue 2 , 01 June 2007 , pp. 234 - 242
Copyright
Copyright © Canadian Mathematical Society 2007

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