Oscillations of Hecke eigenvalues at shifted primes

DOI10.4171/RMI/458zbMath1170.11024arXivmath/0508129OpenAlexW2091423952MaRDI QIDQ854555

Liangyi Zhao

Publication date: 5 December 2006

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0508129

zbMATH Keywords

exponential sumHecke eigenvalues

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Applications of sieve methods (11N36) Estimates on character sums (11L40) Hecke-Petersson operators, differential operators (one variable) (11F25)

Related Items (12)

On exponential sums involving Fourier coefficients of cusp forms over primes ⋮ An exponential sum involving Fourier coefficients of eigenforms for \(\mathrm{SL}(2,\mathbb{Z})\) ⋮ Fourier coefficients at primes twisted with exponential functions ⋮ On the estimation of nonlinear twists of the Liouville function ⋮ Resonance between automorphic forms and exponential functions ⋮ On the distribution of Hecke eigenvalues over Piatetski-Shapiro prime twins ⋮ Oscillations of Fourier coefficients of \(\mathrm{GL}(m)\) Hecke-Maass forms and nonlinear exponential functions at primes ⋮ Nonlinear exponential twists of the Liouville function ⋮ Oscillations of cusp form coefficients over primes ⋮ Oscillations of cusp form coefficients in exponential sums ⋮ Oscillations of Fourier coefficients of cusp forms over primes ⋮ Oscillations of coefficients of primitive cusp forms over some special sequences

Cites Work

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• Cusp forms and eigenfunctions of the Laplacian
• Beiträge zur Theorie der Dirichletreihen, die Spitzenformen zugeordnet sind
• Oscillations of Fourier coefficients of modular forms
• Lectures on a method in the theory of exponential sums
• La conjecture de Weil. I
• Ω-results for sums of Fourier coefficients of cusp forms
• The square mean of Dirichlet series associated with cusp forms
• Mean Value Theorems in Prime Number Theory
• Low lying zeros of families of \(L\)-functions

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