Interprétation combinatoire des moments négatifs des valeurs de fonctions L au bord de la bande critique

DOI10.1016/S0012-9593(03)00024-7zbMath1050.11055MaRDI QIDQ4437944

Emmanuel Royer

Publication date: 3 December 2003

Published in: Annales Scientifiques de l’École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_2003_4_36_4_601_0

zbMATH Keywords

\(L\)-functionsCatalan numbersprimitive modular forms

Mathematics Subject Classification ID

Other combinatorial number theory (11B75) Other Dirichlet series and zeta functions (11M41) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Holomorphic modular forms of integral weight (11F11) Special sequences and polynomials (11B83) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items (8)

Distribution of values of symmetric power \(L\)-functions at the edge of the critical strip ⋮ Absolute values of \(L\)-functions for \(\mathrm{GL}(n, \mathbb{R})\) at the point 1 ⋮ 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 ⋮ \(L\)-functions of automorphic forms and combinatorics: Dyck paths. ⋮ 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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• Coefficients of Maass forms and the Siegel zero. Appendix: An effective zero-free region, by Dorian Goldfeld, Jeffrey Hoffstein and Daniel Lieman
• Zeros of families of automorphic \(L\)-functions close to 1.
• The analytic rank of \(J_0(q)\) and zeros of automorphic \(L\)-functions.
• Small eigenvalues of Laplacian for $Γ_{0}(N)$
• Values of symmetric square L-functions at 1
• THE 'LARGE SIEVE' METHOD AND ITS APPLICATIONS IN THE THEORY OF NUMBERS
• Low lying zeros of families of \(L\)-functions
• Statistics of the random variable \(L(\text{sym}^2f,1)\)

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