L -functions of automorphic forms and combinatorics: Dyck paths

Laurent Habsieger[1]; Emmanuel Royer

  • [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)

Annales de l'Institut Fourier (2004)

  • Volume: 54, Issue: 7, page 2105-2141
  • ISSN: 0373-0956

Abstract

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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 G L ( 2 ) and G L ( 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.

How to cite

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Habsieger, Laurent, and Royer, Emmanuel. "$L$-functions of automorphic forms and combinatorics: Dyck paths." Annales de l'Institut Fourier 54.7 (2004): 2105-2141. <http://eudml.org/doc/116169>.

@article{Habsieger2004,
abstract = {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.},
affiliation = {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)},
author = {Habsieger, Laurent, Royer, Emmanuel},
journal = {Annales de l'Institut Fourier},
keywords = {Symmetric square; modular form; $L$-function; Dyck path; combinatorics; Narayana number; symmetric square; -function},
language = {eng},
number = {7},
pages = {2105-2141},
publisher = {Association des Annales de l'Institut Fourier},
title = {$L$-functions of automorphic forms and combinatorics: Dyck paths},
url = {http://eudml.org/doc/116169},
volume = {54},
year = {2004},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 7
SP - 2105
EP - 2141
AB - 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.
LA - eng
KW - Symmetric square; modular form; $L$-function; Dyck path; combinatorics; Narayana number; symmetric square; -function
UR - http://eudml.org/doc/116169
ER -

References

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  10. E. Royer, Interprétation combinatoire des moments négatifs des valeurs de fonctions L au bord de la bande critique, Annales scientifiques de l'École Normale Supérieure 36 (2003), 601-620 Zbl1050.11055MR2013928
  11. E. Royer, J. Wu, Taille des valeurs de fonctions L de carrés symétriques au bord de la bande critique, (2004) Zbl1147.11027MR2155022
  12. J.-P. Serre, Répartition asymptotique des valeurs propres de l’opérateur de Hecke T p , J. Amer. Math. Soc. 10 (1997), 75-102 Zbl0871.11032MR1396897
  13. R.A. Sulanke, Catalan path statistics having the Narayana distribution, Proceedings of the 7th Conference on Formal Power Series and Algebraic Combinatorics (Noisy-le-Grand, 1995) vol. 180 (1998), 369-389 Zbl0896.05002
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  15. M. Watkins, Computing the modular degree of an elliptic curve, Experiment. Math. 11 (2002), 487-502 Zbl1162.11349MR1969641

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