Weighted Sato-Tate Vertical Distribution of the Satake Parameter of Maass Forms on PGL(N)
Number Theory
2017-01-31 v3
Abstract
We formulate a conjectured orthogonality relation between the Fourier coefficients of Maass forms on PGL(N) for N>=2. Based on the work of Goldfeld-Kontorovich and Blomer for N=3, and on our conjecture for N>=4, we prove a weighted vertical equidistribution theorem (with respect to the generalized Sato-Tate measure) for the Satake parameter of Maass forms at a finite prime. For N=3, the rate of convergence for the equidistribution theorem is obtained.
Cite
@article{arxiv.1303.0889,
title = {Weighted Sato-Tate Vertical Distribution of the Satake Parameter of Maass Forms on PGL(N)},
author = {Fan Zhou},
journal= {arXiv preprint arXiv:1303.0889},
year = {2017}
}