Dirichlet twists of \(\mathrm{GL}_n\)-automorphic \(L\)-functions and hyper-Kloosterman Dirichlet series

DOI10.5802/afst.1687zbMath1494.11050arXiv1903.06690OpenAlexW3208307100MaRDI QIDQ2053319

Jeanine Van Order

Publication date: 29 November 2021

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.06690

zbMATH Keywords

functional equationDirichlet seriesKloosterman sumsanalytic continuationVoronoi summation

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66)

Cites Work

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• Upper and lower bounds at \(s=1\) for certain Dirichlet series with Euler product.
• On Selberg's eigenvalue conjecture
• The Voronoi formula and double Dirichlet series
• Voronoi formulas on GL(n)
• The Voronoi Formula for GL(n, R)
• A general Voronoi summation formula for GL(n,Z)
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• On the Voronoĭ formula for GL(<i>n</i>)
• Upper Bounds on L-Functions at the Edge of the Critical Strip
• The Balanced Voronoi Formulas for $\textrm{GL}(n)$
• \(p\)-adic Fourier theory

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