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 (6)

• Applications of the Kuznetsov formula on GL(3)
• Spectral asymptotics for arithmetic quotients of SL(n,R)/SO(n)
• Low-lying zeroes of Maass form $L$-functions
• Plancherel distribution of Satake parameters of Maass cusp forms on $G{L}_3$
• $L^p$ norms of higher rank eigenfunctions and bounds for spherical functions
• The functional equation of the Jacquet-Shalika integral representation of the local exterior-square $L$-function

Cited by in corpus (9)

• Large values of cusp forms on GL(n)
• On the distribution of Satake parameters for Siegel modular forms
• Asymptotic behavior of supercuspidal representations and Sato-Tate equidistribution for families
• Limit multiplicities for ${\mathrm{SL}}_2({\mathcal{O}}_F)$ in ${\mathrm{SL}}_2({\mathbb{R}}^{r_1}\oplus {\mathbb{C}}^{r_2})$
• An estimate for spherical functions on $\mathrm{SL}(3,\mathbb{R})$
• An Asymptotic Orthogonality Relation for $\mathrm{GL}(n,\mathbb{R})$
• Spectral summation formula for GSp(4) and moments of spinor L-functions
• 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
• Asymptotics of automorphic spectra and the trace formula