A sieve method for shifted convolution sums

DOI10.1215/00127094-2009-002zbMath1218.11089arXiv0809.1669OpenAlexW2963200100MaRDI QIDQ1000600

Roman Holowinsky

Publication date: 10 February 2009

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

Full work available at URL: https://arxiv.org/abs/0809.1669

zbMATH Keywords

eigenvaluessieve methodHecke-Maass cusp formshifted convolution sum

Mathematics Subject Classification ID

Fourier coefficients of automorphic forms (11F30) Applications of sieve methods (11N36) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36)

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Some recents advances on Duke’s equidistribution theorems, Quantum variance for dihedral Maass forms, Bounds on shifted convolution sums for Hecke eigenforms, Mass equidistribution for automorphic forms of cohomological type on 𝐺𝐿₂, Shifted convolution sums of Fourier coefficients with divisor functions, Summing Hecke eigenvalues over polynomials, On triple correlations of Fourier coefficients of cusp forms, Shifted convolution sums for \(\mathrm{GL}(3)\times\mathrm{GL}(2)\), The Weyl bound for triple product \(L\)-functions, Shifted convolution sums involving theta series, Sums of \(k\)-th powers and Fourier coefficients of cusp forms, On certain kernel functions and shifted convolution sums of the Fourier coefficients, On averages of Fourier coefficients of Maass cusp forms, Mass equidistribution of Hilbert modular eigenforms, Shifted convolution of cusp-forms with \(\theta \)-series, Exponential sums with multiplicative coefficients without the Ramanujan conjecture, Average of Dirichlet coefficients of cuspidal representations related to \(\mathrm{GL}(2)\), Power sums of Hecke eigenvalues of Maass cusp forms, A shifted convolution sum for \(\mathrm{GL}(3) \times \mathrm{GL}(2)\), Shifted convolution sums related to Hecke-Maass forms, When Kloosterman sums meet Hecke eigenvalues, Shifted convolution sums of Fourier coefficients with squarefull kernel functions, Strong orthogonality between the Möbius function, additive characters and Fourier coefficients of cusp forms

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