We give a combinatorial interpretation for the positive moments of the values at the edge of the critical strip of the -functions of modular forms of and . 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 de formes modulaires de et . 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.
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
@article{AIF_2004__54_7_2105_0, author = {Habsieger, Laurent and Royer, Emmanuel}, title = {$L$-functions of automorphic forms and combinatorics: {Dyck} paths}, journal = {Annales de l'Institut Fourier}, pages = {2105--2141}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {7}, year = {2004}, doi = {10.5802/aif.2076}, mrnumber = {2139690}, zbl = {1131.11340}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2076/} }
TY - JOUR AU - Habsieger, Laurent AU - Royer, Emmanuel TI - $L$-functions of automorphic forms and combinatorics: Dyck paths JO - Annales de l'Institut Fourier PY - 2004 SP - 2105 EP - 2141 VL - 54 IS - 7 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2076/ DO - 10.5802/aif.2076 LA - en ID - AIF_2004__54_7_2105_0 ER -
%0 Journal Article %A Habsieger, Laurent %A Royer, Emmanuel %T $L$-functions of automorphic forms and combinatorics: Dyck paths %J Annales de l'Institut Fourier %D 2004 %P 2105-2141 %V 54 %N 7 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2076/ %R 10.5802/aif.2076 %G en %F AIF_2004__54_7_2105_0
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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