For simply connected simple Chevalley groups over Q, the cuspidal Weyl law for congruence subgroups holds with remainder O(T^{d-δ}) for some δ > 0, where d is the dimension of the symmetric space.
Sato-Tate equidistribution for families of Hecke-Maass forms on SL(n,R)/SO(n)
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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.
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On the remainder term of the Weyl law for congruence subgroups of Chevalley groups
For simply connected simple Chevalley groups over Q, the cuspidal Weyl law for congruence subgroups holds with remainder O(T^{d-δ}) for some δ > 0, where d is the dimension of the symmetric space.