Weighted Sato-Tate vertical distribution of the Satake parameter of Maass forms on \(\mathrm{PGL}(N)\)

DOI10.1007/s11139-013-9535-6zbMath1326.11021arXiv1303.0889OpenAlexW3102827701MaRDI QIDQ486600

Fan Zhou

Publication date: 16 January 2015

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

Full work available at URL: https://arxiv.org/abs/1303.0889

zbMATH Keywords

equidistributiontrace formulaorthogonality relationautomorphic formSato-Tate conjectureMaass formSato-Tate measureKuznetsov trace formulaRamanujan conjectureCasselman-Shalika formulaSatake parameter

Mathematics Subject Classification ID

Other groups and their modular and automorphic forms (several variables) (11F55) Fourier coefficients of automorphic forms (11F30) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (9)

Hecke-Maass cusp forms on \(\operatorname{PGL}_n\) of large levels with non-vanishing \(L\)-values ⋮ An orthogonality relation for a thin family of GL(3) Maass forms ⋮ Absolute values of \(L\)-functions for \(\mathrm{GL}(n, \mathbb{R})\) at the point 1 ⋮ On the distribution of Satake parameters for Siegel modular forms ⋮ On signs of Fourier coefficients of Hecke-Maass cusp forms on 𝐺𝐿₃ ⋮ Weighted Distribution of Low-lying Zeros of GL(2) -functions ⋮ Fourier coefficients of \(\mathrm{GL}(N)\) automorphic forms in arithmetic progressions ⋮ Applications of analytic newvectors for \(\operatorname{GL}(N)\) ⋮ An orthogonality relation for (with an appendix by Bingrong Huang)

Uses Software

• GL(n)pack

Cites Work

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