Mollification and non-vanishing of automorphic \(L\)-functions at the primary level

DOI10.1016/J.JNT.2011.06.006zbMath1294.11064OpenAlexW2058917296MaRDI QIDQ643534

D. Rouymi

Publication date: 2 November 2011

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2011.06.006

zbMATH Keywords

modular formsFourier coefficientsmollificationDeligne's inequalitynon-vanishing of automorphic \(L\)-functions

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Fourier coefficients of automorphic forms (11F30) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Applications of automorphic functions and forms to multiplicative problems (11N75)

Related Items (4)

Moments of central 𝐿-values for Maass forms over imaginary quadratic fields ⋮ Non-vanishing of automorphic \(L\)-functions of prime power level ⋮ Non-vanishing of Maass form $L$-functions at the central point ⋮ A uniform asymptotic formula for the second moment of primitive \(L\)-functions on the critical line

Cites Work

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• Mollification of the fourth moment of automorphic \(L\)-functions and arithmetic applications.
• The critical order of vanishing of automorphic \(L\)-functions with large level
• On the positivity of the central critical values of automorphic \(L\)-functions for \(GL(2)\)
• Average values of symmetric square \(L\)-functions at the edge of the critical strip
• Formules de trace et non-annulation de fonctions L automorphes au niveau p^ν
• A lower bound for the rank of $J_0(q)$

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