On shifted convolutions of \(\zeta^3(s)\) with automorphic \(L\)-functions

DOI10.1215/S0012-7094-95-07711-4zbMath0855.11024OpenAlexW1554501108MaRDI QIDQ1895991

Nigel J. E. Pitt

Publication date: 30 January 1997

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-95-07711-4

zbMATH Keywords

Riemann zeta functionexponential sumsautomorphic \(L\)-functionsKloosterman sumsshifted convolution

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Other Dirichlet series and zeta functions (11M41) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Applications of automorphic functions and forms to multiplicative problems (11N75)

Related Items (21)

The fifth moment of modular \(L\)-functions ⋮ Averages of shifted convolution sums for \(\mathrm{GL}(3)\times \mathrm{GL}(2)\) ⋮ Shifted convolution sums for \(\mathrm{GL}(3)\times\mathrm{GL}(2)\) ⋮ SHIFTED CONVOLUTION SUM OF AND THE FOURIER COEFFICIENT OF HECKE–MAASS FORMS ⋮ Shifted convolution sums for higher rank groups ⋮ Estimates for the shifted convolution sum involving Fourier coefficients of cusp forms of half-integral weight ⋮ Averages of shifted convolution sums for arithmetic functions ⋮ A study in sums of products ⋮ A SHIFTED CONVOLUTION SUM OF AND THE FOURIER COEFFICIENTS OF HECKE–MAASS FORMS II ⋮ Sums of \(k\)-th powers and Fourier coefficients of cusp forms ⋮ Triple correlation sums of coefficients of cuspidal forms ⋮ Unnamed Item ⋮ A nonsplit sum of coefficients of modular forms ⋮ Shifted convolution sums for \(\mathrm{SL}(m)\) ⋮ On an analogue of Titchmarsh’s divisor problem for holomorphic cusp forms ⋮ Averages of shifted convolutions of general divisor sums involving Hecke eigenvalues ⋮ A shifted convolution sum for \(\mathrm{GL}(3) \times \mathrm{GL}(2)\) ⋮ Shifted convolution sums of \(\mathrm{GL}(m)\) cusp forms with \(\Theta\)-series ⋮ Uniform Titchmarsh divisor problems ⋮ Estimates of shifted convolution sums involving Fourier coefficients of Hecke–Maass eigenform ⋮ Algebraic twists of modular forms and Hecke orbits

Cites Work

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• Exponential sums and Newton polyhedra: cohomology and estimates
• Cusp forms and eigenfunctions of the Laplacian
• Kloosterman sums and Fourier coefficients of cusp forms
• On exponential sums in finite fields. II
• Exponential sums on \((\mathbb{G}_ m)^ n\)
• La conjecture de Weil. I
• Small eigenvalues of Laplacian for $Γ_{0}(N)$
• Exponential sums and Newton polyhedra
• On Certain L-Functions
• Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116)
• On the Rationality of the Zeta Function of an Algebraic Variety

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