Equidistribution of Fourier coefficients of square and cube symmetric \(L\)-functions
type: Item
instance of: scholarly article
title: Equidistribution of Fourier coefficients of square and cube symmetric \(L\)-functions
zbMATH Open document ID: 1226.11061
author: Sami Omar
author: Kamel Mazhouda
published in: The Ramanujan Journal
publication date: 2009-11-16T00:00:00Z
review text: The main theorems of this work are three equidistribution results about the Fourier coefficients of square and cube symmetric \(L\)-functions of primitive cusp forms. The first provides a new proof of an equidistribution result for the Fourier coefficients of symmetric square \(L\)-functions implied by the work of \textit{P. Sarnak} [Analytic number theory and diophantine problems, Proc. Conf., Stillwater/Okla. 1984, Prog. Math. 70, 321--331 (1987; Zbl 0628.10028)], \textit{J.-P. Serre} [J. Am. Math. Soc. 10, No.1, 75--102 (1997; Zbl 0871.11032)] and \textit{J. B. Conrey, W. Duke} and \textit{D. W. Farmer} [Acta Arith. 78, No. 4, 405--409 (1997; Zbl 0876.11020)]. The new proof does not use their work. The analogue for symmetric cube \(L\)-cubes is the content of the second main theorem of the paper. In the final theorem, it is proved that the Fourier coefficients of symmetric square \(L\)-functions are ``harmonically equidistributed'' according to the definition given in the paper.
reviewed by: Nikolaos Diamantis
Mathematics Subject Classification ID: 11F25
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 11F30
Mathematics Subject Classification ID: 11M41
Mathematics Subject Classification ID: 11N36
zbMATH DE Number: 5633534
zbMATH Keywords: symmetric square L-functions
zbMATH Keywords: symmetric cube L-functions
zbMATH Keywords: equidistribution
MaRDI profile type: Publication
full work available at URL: s11139-009-9157-1
OpenAlex ID: W2014871914
cites work: The distribution of the eigenvalues of Hecke operators
cites work: Low lying zeros of families of \(L\)-functions
cites work: Facteurs $\bbfQ$-simples de $J_{0}(N)$ de grande dimension et de grand rang
cites work: Special values of symmetric power \(L\)-functions and Hecke eigenvalues
cites work: Average values of symmetric square \(L\)-functions at the edge of the critical strip
cites work: Répartition asymptotique des valeurs propres de l’opérateur de Hecke 𝑇_𝑝
DOI: 10.1007/S11139-009-9157-1
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description: scientific article; zbMATH DE number 5633534