Distribution of cusp sections in the Hilbert modular orbifold
Number Theory
2011-12-07 v1
Abstract
Let K be a number field, let M be the Hilbert modular orbifold of K, and let m(q) be the probability measure uniformly supported on the cusp cross sections of M at height q. We generalize a method of Zagier and show that m(q) distributes uniformly with respect to the normalized Haar measure m on M as q tends to zero, and relate the rate by which m(q) approaches m to the Riemann hypothesis for the Dedekind zeta function of K.
Cite
@article{arxiv.1112.1146,
title = {Distribution of cusp sections in the Hilbert modular orbifold},
author = {Samuel Estala Arias},
journal= {arXiv preprint arXiv:1112.1146},
year = {2011}
}
Comments
21 pages