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March, 2005 Taille des valeurs de fonctions $L$ de carrés symétriques au bord de la bande critique
Emmanuel Royer, Jie Wu
Rev. Mat. Iberoamericana 21(1): 263-312 (March, 2005).

Abstract

For each weight $k$ and level $N$ square free and without small prime factors, we prove the existence of primitive forms $f_+$ and $f_-$ of weight $k$ and level $N$ such that $$ L(1,\sym^2f_+)\gg_{k}[\log\log(3N)]^{3} $$ and $$ L(1,\sym^2f_-)\ll_{k}[\log\log(3N)]^{-1}. $$ The result comes from a delicate study of the moments of $L(1,\sym^2 f)$. This study gives also results for squarefree levels but with small prime factors. It provides counterexamples to the equivalence between harmonic and natural means.

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Emmanuel Royer. Jie Wu. "Taille des valeurs de fonctions $L$ de carrés symétriques au bord de la bande critique." Rev. Mat. Iberoamericana 21 (1) 263 - 312, March, 2005.

Information

Published: March, 2005
First available in Project Euclid: 22 April 2005

zbMATH: 1147.11027
MathSciNet: MR2155022

Subjects:
Primary: 11F12 , 11F25 , 11F67 , 11M41 , 11N36 , 11N37

Keywords: carré symétrique , fonction $L$ , forme automorphe , valeur spéciale

Rights: Copyright © 2005 Departamento de Matemáticas, Universidad Autónoma de Madrid

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