Functiones et Approximatio Commentarii Mathematici

Le premier coefficient négatif des fonctions $L$ de puissances symétriques

Kamel Mazhouda, Khadija Mbarki, and Jie Wu

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Résumé

Désignons par $\lambda_{{\rm sym}^mf}(n)$ le $n$-ème coefficient dans la série de Dirichlet représentant la fonction $L$ de puissances symétriques $L(s, {\rm sym}^mf)$ associée à une forme primitive $f$ de poids $k$ et de niveau $N$. Dans ce papier, on étudie la taille de l'entier le plus petit $n$ tel que $\lambda_{{\rm sym}^mf}(n)<0$ et $(n,N)=1$. En désignant par $n_{{\rm sym}^mf}$ cet entier, on montre que $$ n_{{\rm sym}^3f} \ll (k^{4} N^3)^{6/31} \qquad\text{et}\qquad n_{{\rm sym}^4f} \ll (k^{4} N^4)^{5/36}, $$ où les constantes impliquées sont absolues.

Article information

Source
Funct. Approx. Comment. Math., Volume 56, Number 2 (2017), 239-258.

Dates
First available in Project Euclid: 28 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.facm/1490688013

Digital Object Identifier
doi:10.7169/facm/1609

Mathematical Reviews number (MathSciNet)
MR3660962

Zentralblatt MATH identifier
06864157

Subjects
Primary: 11F12: Automorphic forms, one variable 11F30: Fourier coefficients of automorphic forms
Secondary: 11M41: Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}

Keywords
Formes modulaires fonctions $L$ coefficients de Fourier signes

Citation

Mazhouda, Kamel; Mbarki, Khadija; Wu, Jie. Le premier coefficient négatif des fonctions $L$ de puissances symétriques. Funct. Approx. Comment. Math. 56 (2017), no. 2, 239--258. doi:10.7169/facm/1609. https://projecteuclid.org/euclid.facm/1490688013


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