The average behavior of Fourier coefficients of cusp forms over sparse sequences

DOI10.1090/S0002-9939-09-09855-4zbMath1225.11059OpenAlexW1992636931MaRDI QIDQ5322848

Huixue Lao, Ayyadurai Sankaranarayanan

Publication date: 23 July 2009

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-09-09855-4

zbMATH Keywords

Rankin-Selberg \(L\)-functionFourier coefficients of cusp formssymmetric power \(L\)-function

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)

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Cites Work

• La conjecture de Weil. I
• Cuspidality of symmetric powers with applications.
• Fundamental properties of symmetric square \(L\)-functions. I.
• Functorial products for \(\text{GL}_2\times \text{GL}_3\) and the symmetric cube for \(\text{GL}_2\).
• On a sum involving Fourier coefficients of cusp forms
• Behavior of automorphic \(L\)-functions at the center of the critical strip
• A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• A density theorem on automorphic $L$-functions and some applications
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