Sato-Tate equidistribution for families of Hecke-Maass forms on SL(n,R)/SO(n)

Abstract

We establish the Sato-Tate equidistribution of Hecke eigenvalues on average for families of Hecke--Maass cusp forms on SL(n,R)/SO(n). For each of the principal, symmetric square and exterior square L-functions we verify that the families are essentially cuspidal and deduce the level distribution with restricted support of the low-lying zeros. We also deduce average estimates toward Ramanujan.

References in corpus (2)

• Plancherel distribution of Satake parameters of Maass cusp forms on $G{L}_3$
• The functional equation of the Jacquet-Shalika integral representation of the local exterior-square $L$-function

Cited by in corpus (8)

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• Some Results in the Theory of Low-lying Zeros: Determining the 1-level density, identifying the group symmetry and the arithmetic of moments of Satake parameters
• An Asymptotic Orthogonality Relation for $\mathrm{GL}(n,\mathbb{R})$
• Asymptotics of automorphic spectra and the trace formula
• An estimate for spherical functions on $\mathrm{SL}(3,\mathbb{R})$
• Spectral summation formula for GSp(4) and moments of spinor L-functions