L-functions of automorphic forms and combinatorics: Dyck paths
Annales de l'Institut Fourier, Volume 54 (2004) no. 7, pp. 2105-2141.

We give a combinatorial interpretation for the positive moments of the values at the edge of the critical strip of the L-functions of modular forms of GL(2) and GL(3). We deduce some results about the asymptotics of these moments. We extend this interpretation to the moments twisted by the eigenvalues of Hecke operators.

Nous donnons une interprétation combinatoire pour les moments positifs des valeurs au bord de la bande critique des fonctions L de formes modulaires de GL(2) et GL(3). Nous en déduisons des résultats concernant la taille asymptotique de ces moments. Nous étendons cette interprétation aux moments tordus par les valeurs propres des opérateurs de Hecke.

DOI: 10.5802/aif.2076
Classification: 11F11, 11F12, 11F67, 11M41, 05A15, 05A19, 11B75, 11B83
Keywords: Symmetric square, modular form, $L$-function, Dyck path, combinatorics, Narayana number
Mot clés : carré symétrique, forme modulaire, fonction $L$, chemin de Dyck, combinatoire, nombre de Narayana
Habsieger, Laurent 1; Royer, Emmanuel 

1 Université Claude Bernard Lyon I, Institut Girard Desargues, CNRS UMR 5028, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex (France), Université Paul Valéry Montpellier III, MIAp, 34199 Montpellier cedex 5 (France)
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Habsieger, Laurent; Royer, Emmanuel. $L$-functions of automorphic forms and combinatorics: Dyck paths. Annales de l'Institut Fourier, Volume 54 (2004) no. 7, pp. 2105-2141. doi : 10.5802/aif.2076. http://archive.numdam.org/articles/10.5802/aif.2076/

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