On Selberg's limit theorem for \(L\)-functions over a family of \(\mathrm{GL} (n)\) Hecke-Maass cusp forms

DOI10.1007/s11139-022-00590-4zbMath1505.11077OpenAlexW4293081441WikidataQ113900547 ScholiaQ113900547MaRDI QIDQ2097516

Yuk-Kam Lau, Yingnan Wang, Guo-Hua Chen

Publication date: 14 November 2022

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-022-00590-4

zbMATH Keywords

\(L\)-functionsautomorphic forms for \(\mathrm{GL} (n)\)Selberg's limit theorem

Mathematics Subject Classification ID

Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Automorphic forms, one variable (11F12) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Cites Work

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• Statistics of Hecke eigenvalues for \(\mathrm{GL}(n)\)
• Value distribution of \(L\)-functions
• Absolute values of \(L\)-functions for \(\mathrm{GL}(n, \mathbb{R})\) at the point 1
• Selberg's central limit theorem for \(\log|\zeta(1/2+it)|\)
• On Selberg's eigenvalue conjecture
• Sato-Tate equidistribution for families of Hecke-Maass forms on \(\mathrm{SL}(n,\mathbb{R})/\mathrm{SO}(n)\)
• A \(\mathrm{GL}_3\) analog of Selberg's result on \(S(t)\)
• Voronoi formulas on GL(n)
• Analytic $L$-functions: Definitions, theorems, and connections
• Upper Bounds on L-Functions at the Edge of the Critical Strip
• Automorphic Forms and L-Functions for the GroupGL(n, R)

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