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15 March 2002 Cuspidality of symmetric powers with applications
Henry H. Kim, Freydoon Shahidi
Duke Math. J. 112(1): 177-197 (15 March 2002). DOI: 10.1215/S0012-9074-02-11215-0

Abstract

The purpose of this paper is to prove that the symmetric fourth power of a cusp form on ${\rm GL}(2)$, whose existence was proved earlier by the first author, is cuspidal unless the corresponding automorphic representation is of dihedral, tetrahedral, or octahedral type. As a consequence, we prove a number of results toward the Ramanujan-Petersson and Sato-Tate conjectures. In particular, we establish the bound $q\sp {1/9}\sb v$ for unramified Hecke eigenvalues of cusp forms on ${\rm GL}(2)$. Over an arbitrary number field, this is the best bound available at present.

Citation

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Henry H. Kim. Freydoon Shahidi. "Cuspidality of symmetric powers with applications." Duke Math. J. 112 (1) 177 - 197, 15 March 2002. https://doi.org/10.1215/S0012-9074-02-11215-0

Information

Published: 15 March 2002
First available in Project Euclid: 18 June 2004

zbMATH: 1074.11027
MathSciNet: MR1890650
Digital Object Identifier: 10.1215/S0012-9074-02-11215-0

Subjects:
Primary: 11F70
Secondary: 11F30 , 11R42

Rights: Copyright © 2002 Duke University Press

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Vol.112 • No. 1 • 15 March 2002
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