Average estimates and sign change of Fourier coefficients of cusp forms at integers represented by binary quadratic form of fixed discriminant

DOI10.1007/S12044-024-00782-6zbMATH Open1544.11046MaRDI QIDQ6566132

Lalit Vaishya

Publication date: 3 July 2024

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

zbMATH Keywords

binary quadratic formasymptotic behaviourRankin-Selberg \(L\)-functionsymmetric power \(L\)-functionFourier coefficients of cusp form

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) (zeta (s)) and (L(s, chi)) (11M06) Fourier coefficients of automorphic forms (11F30) Holomorphic modular forms of integral weight (11F11)

Cites Work

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• The first simultaneous sign change and non-vanishing of Hecke eigenvalues of newforms
• Average behavior of Fourier coefficients of cusp forms over sum of two squares
• The sixth and eighth moments of Fourier coefficients of cusp forms
• On the signs of Fourier coefficients of cusp forms
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• The fourth moment of the Ramanujan tau-function
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• Signs of Fourier coefficients of cusp forms at integers represented by an integral binary quadratic form
• Signs of Fourier coefficients of cusp form at sum of two squares
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• Bemerkungen über eine Dirichletsche Reihe, die mit der Theorie der Modulformen nahe verbunden ist.
• On Higher Moments of Fourier Coefficients of Holomorphic Cusp Forms
• On modular signs
• Integral power sums of Hecke eigenvalues
• On signs of Fourier coefficients of cusp forms
• Average behavior of Fourier coefficients of cusp forms
• The growth rate of the Dedekind Zeta-function on the critical line
• The square mean of Dirichlet series associated with cusp forms
• THE FIRST NEGATIVE HECKE EIGENVALUE
• Sign changes of Fourier coefficients of half-integral weight cusp forms
• A density theorem on automorphic $L$-functions and some applications

Related Items (1)

Oscillations of Fourier coefficients over the sparse set of integers

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