On sums involving coefficients of automorphic $L$-functions

DOI10.1090/S0002-9939-09-09845-1zbMath1247.11065OpenAlexW2010420491MaRDI QIDQ3395558

Guangshi Lü

Publication date: 11 September 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-09-09845-1

zbMATH Keywords

symmetric square \(L\)-functionautomorphic \(L\)-functionRamanujan conjecture

Mathematics Subject Classification ID

Fourier coefficients of automorphic forms (11F30) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Holomorphic modular forms of integral weight (11F11)

Related Items (11)

Fourier coefficients of symmetric power \(L\)-functions ⋮ Oscillations of coefficients of Dirichlet series attached to automorphic forms ⋮ Cancellation of two classes of dirichlet coefficients over Beatty sequences ⋮ Estimates for coefficients of certain \(L\)-functions ⋮ Mean value of Dirichlet series coefficients of Rankin-Selberg \(L\)-functions ⋮ First moments of Fourier coefficients of \(\mathrm{GL}(r)\) cusp forms ⋮ Mean value theorem connected with Fourier coefficients of Hecke-Maass forms for SL(m, ℤ) ⋮ On sums involving Fourier coefficients of Maass forms for \(\mathrm{SL}(3,\mathbb Z)\) ⋮ On exponential sums for coefficients of general L-functions ⋮ Sums of Fourier coefficients related to Hecke eigencusp forms ⋮ On sums of Fourier coefficients of Maass cusp forms

Cites Work

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• Weak subconvexity for central values of \(L\)-functions
• A nonvanishing result for twists of \(L\)-functions of \(\text{GL}(n)\)
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• Functional equations with multiple gamma factors and the average order of arithmetical functions
• Zeta functions of simple algebras
• On Euler Products and the Classification of Automorphic Forms II
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• Summation Formulae for Coefficients of L-functions
• Cancellation in additively twisted sums on GL(n)
• Automorphic Forms and L-Functions for the GroupGL(n, R)

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