The Prime Geodesic Theorem in Arithmetic Progressions
Number Theory
2024-11-18 v1
Abstract
We address the prime geodesic theorem in arithmetic progressions, and resolve conjectures of Golovchanski\u{\i}-Smotrov (1999). In particular, we prove that the traces of closed geodesics on the modular surface do not equidistribute in the reduced residue classes of a given modulus.
Cite
@article{arxiv.2309.04186,
title = {The Prime Geodesic Theorem in Arithmetic Progressions},
author = {Dimitrios Chatzakos and Gergely Harcos and Ikuya Kaneko},
journal= {arXiv preprint arXiv:2309.04186},
year = {2024}
}
Comments
11 pages, LaTeX2e