Sato-Tate Problem for GL(3)

Based upon the work of Goldfeld and Kontorovich on the Kuznetsov trace formula of Maass forms for SL(3, $Z$), we prove a weighted vertical equidistribution theorem (with respect to the generalized Sato-Tate measure) for the pth Hecke eigenvalue of Maass forms, with the rate of convergence. With a conjectured orthogonality relation between the Fourier coefficients of Maass forms for SL(N, $Z$) for N ≥ 4, we generalize the above equidistribution theorem to N ≥ 4.