Shifted convolution sums for \(\mathrm{SL}(m)\)

DOI10.1007/s00229-019-01166-1zbMath1444.11073OpenAlexW2985855640MaRDI QIDQ2004023

Guangwei Hu, Guangshi Lü

Publication date: 14 October 2020

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-019-01166-1

zbMATH Keywords

Fourier coefficientsshifted convolution sums

Mathematics Subject Classification ID

Fourier coefficients of automorphic forms (11F30) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Holomorphic modular forms of integral weight (11F11) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Cites Work

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• Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three
• Shifted convolution sums for \(\mathrm{GL}(3)\times\mathrm{GL}(2)\)
• On shifted convolutions of \(\zeta^3(s)\) with automorphic \(L\)-functions
• Shifted convolution sums for higher rank groups
• The Asymptotic Formula in Waring’s Problem
• The Voronoi Formula for GL(n, R)
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• Cancellation in additively twisted sums on GL(n)
• Shifted convolution of cusp-forms with \(\theta \)-series
• Shifted convolution of cusp-forms with \(\theta \)-series

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