Shifted convolution sums for higher rank groups

DOI10.1515/forum-2017-0269zbMath1470.11072OpenAlexW2896804555MaRDI QIDQ2418032

Guangshi Lü, Yujiao Jiang

Publication date: 31 May 2019

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/forum-2017-0269

zbMATH Keywords

theta functionscusp formsshifted convolution sums

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Theta series; Weil representation; theta correspondences (11F27) Fourier coefficients of automorphic forms (11F30) Holomorphic modular forms of integral weight (11F11)

Related Items (7)

THE FOURIER COEFFICIENTS OF Θ‐SERIES IN ARITHMETIC PROGRESSIONS ⋮ Sums of \(k\)-th powers and Fourier coefficients of cusp forms ⋮ Shifted convolution sums for \(\mathrm{SL}(m)\) ⋮ Average behavior of the triple divisor function over values of quadratic form ⋮ Sums of \(k\)-th powers and the Whittaker-Fourier coefficients of automorphic forms ⋮ Shifted convolution sums of \(\mathrm{GL}(m)\) cusp forms with \(\Theta\)-series ⋮ Jutila's circle method and \(\mathrm{GL}(2) \times \mathrm{GL}(2)\) shifted convolution sums

Cites Work

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• On the Fourier-Walsh spectrum of the Moebius function
• Shifted convolution sums for \(\mathrm{GL}(3)\times\mathrm{GL}(2)\)
• Automorphic distributions, \(L\)-functions, and Voronoi summation for \(\text{GL}(3)\)
• Resonance and rapid decay of exponential sums of Fourier coefficients of a Maass form for \(\mathrm{GL}_m(\mathbb Z)\)
• The hyper-Kloosterman sum
• A nonvanishing result for twists of \(L\)-functions of \(\text{GL}(n)\)
• Modularity of the Rankin-Selberg \(L\)-series, and multiplicity one for \(\mathrm{SL}(2)\)
• La conjecture de Weil. I
• On shifted convolutions of \(\zeta^3(s)\) with automorphic \(L\)-functions
• The Voronoi formula and double Dirichlet series
• The Voronoi Formula for GL(n, R)
• The average order of a class of arithmetic functions over arithmetic progressions with applications to quadratic forms.
• An Additive Divisor Problem
• On Euler Products and the Classification of Automorphic Representations I
• The Fourth Power Moment of the Riemann Zeta Function
• Über die Darstellungen einer Zahl als Differenz von zwei Produkten.
• Shifted Convolution Sums of GL3 Cusp Forms with θ-Series
• A general Voronoi summation formula for GL(n,Z)
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• Automorphic Forms and L-Functions for the GroupGL(n, R)
• The Mean Value of the Zeta-Function on the Critical Line
• On the Representations of a Number as the Sum of Three Squares
• Shifted convolution of cusp-forms with \(\theta \)-series
• Shifted convolution of cusp-forms with \(\theta \)-series

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