\(L\)-functions of automorphic forms and combinatorics: Dyck paths.

DOI10.5802/aif.2076zbMath1131.11340OpenAlexW2189064094MaRDI QIDQ1774092

Laurent Habsieger, Emmanuel Royer

Publication date: 29 April 2005

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2004__54_7_2105_0

zbMATH Keywords

combinatoricsmodular form\(L\)-functionDyck pathsymmetric squareNarayana number

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Other combinatorial number theory (11B75) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Holomorphic modular forms of integral weight (11F11) Asymptotic enumeration (05A16)

Related Items

Distribution of values of symmetric power \(L\)-functions at the edge of the critical strip, Values of automorphic \(L\)-functions with prime power level at the point \(s=1\), A density theorem on automorphic $L$-functions and some applications, Special values of symmetric power \(L\)-functions and Hecke eigenvalues, Distribution of values at 1 of symmetric power $L$-functions of Maass cusp forms, Average values of symmetric square \(L\)-functions at the edge of the critical strip

Cites Work

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• Computing modular degrees using \(L\)-functions
• Catalan path statistics having the Narayana distribution
• Average values of symmetric square \(L\)-functions at the edge of the critical strip
• Values of symmetric square L-functions at 1
• Interprétation combinatoire des moments négatifs des valeurs de fonctions L au bord de la bande critique
• Upper Bounds for  L(1,  )
• Computing the Modular Degree of an Elliptic Curve
• Répartition asymptotique des valeurs propres de l’opérateur de Hecke 𝑇_𝑝
• Low lying zeros of families of \(L\)-functions
• Statistics of the random variable \(L(\text{sym}^2f,1)\)