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

Jasmin Matz, Nicolas Templier

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 an…