Sato-Tate equidistribution for families of Hecke-Maass forms on \(\mathrm{SL}(n,\mathbb{R})/\mathrm{SO}(n)\)

DOI10.2140/ant.2021.15.1343zbMath1480.11061arXiv1505.07285OpenAlexW3206165783MaRDI QIDQ2239227

Nicolas Templier, Jasmin Matz

Publication date: 3 November 2021

Published in: Algebra \& Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.07285

zbMATH Keywords

\(L\)-functionsautomorphic formsArthur-Selberg trace formulaSato-Tate equidistribution

Mathematics Subject Classification ID

Linear algebraic groups over global fields and their integers (20G30) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Spherical harmonics (33C55) Harmonic analysis and spherical functions (43A90)

Related Items (12)

Almost holomorphic Poincaré series corresponding to products of harmonic Siegel-Maass forms ⋮ On the distribution of Satake parameters for Siegel modular forms ⋮ On signs of Fourier coefficients of Hecke-Maass cusp forms on 𝐺𝐿₃ ⋮ Lower bounds for Maass forms on semisimple groups ⋮ On Sarnak’s Density Conjecture and Its Applications ⋮ The density hypothesis for horizontal families of lattices ⋮ Weighted Distribution of Low-lying Zeros of GL(2) -functions ⋮ Statistics of Hecke eigenvalues for \(\mathrm{GL}(n)\) ⋮ Asymptotic behavior of supercuspidal representations and Sato-Tate equidistribution for families ⋮ Limit multiplicities for \({\text{SL}}_2(\mathcal{O}_F)\) in \({\text{SL}}_2(\mathbb{R}^{r_1}\oplus\mathbb{C}^{R_2})\) ⋮ On Selberg's limit theorem for \(L\)-functions over a family of \(\mathrm{GL} (n)\) Hecke-Maass cusp forms ⋮ Low-lying zeros of \(L\)-functions for quaternion algebras

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