JournalsrmiVol. 21, No. 1pp. 263–312

Taille des valeurs de fonctions LL de carrés symétriques au bord de la bande critique

  • Emmanuel Royer

    Université de Montpellier II, France
  • Jie Wu

    Université Henri Poincaré, Vandoeuvre lès Nancy, France
Taille des valeurs de fonctions $L$ de carrés symétriques au bord de la bande critique cover
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Abstract

For each weight kk and level NN square free and without small prime factors, we prove the existence of primitive forms f+f_+ and ff_- of weight kk and level NN such that

L(1,\sym2f+)k[loglog(3N)]3L(1,\sym^2f_+)\gg_{k}[\log\log(3N)]^{3}

and

L(1,\sym2f)k[loglog(3N)]1.L(1,\sym^2f_-)\ll_{k}[\log\log(3N)]^{-1}.

The result comes from a delicate study of the moments of L(1,\sym2f)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.

Cite this article

Emmanuel Royer, Jie Wu, Taille des valeurs de fonctions LL de carrés symétriques au bord de la bande critique. Rev. Mat. Iberoam. 21 (2005), no. 1, pp. 263–312

DOI 10.4171/RMI/423