Exponential sums involving automorphic forms for \(\mathrm{GL}(3)\) over arithmetic progressions

DOI10.1007/s11464-018-0732-xzbMath1440.11149OpenAlexW2896850491WikidataQ115602153 ScholiaQ115602153MaRDI QIDQ1731903

Xiaoguang He

Publication date: 14 March 2019

Published in: Frontiers of Mathematics in China (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11464-018-0732-x

zbMATH Keywords

arithmetic progressionexponential sumautomorphic forms for \(\mathrm{GL}(3)\)

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Gauss and Kloosterman sums; generalizations (11L05) Fourier coefficients of automorphic forms (11F30)

Uses Software

• GL(n)pack

Cites Work

• Unnamed Item
• Resonance between automorphic forms and exponential functions
• Automorphic distributions, \(L\)-functions, and Voronoi summation for \(\text{GL}(3)\)
• On some exponential sums involving Maass forms over arithmetic progressions
• The central value of the Rankin-Selberg \(L\)-functions
• Exponential sums involving Maass forms
• Voronoi formulas on GL(n)
• The Voronoi Formula for GL(n, R)
• On the structure of the Selberg class, VI: non-linear twists
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• ASYMPTOTIC VORONOI'S SUMMATION FORMULAS AND THEIR DUALITY FOR SL₃(ℤ)
• Automorphic Forms and L-Functions for the GroupGL(n, R)
• Resonance of automorphic forms for 𝐺𝐿(3)
• Low lying zeros of families of \(L\)-functions

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