English

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.

Keywords

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

R2 v1 2026-06-28T12:16:00.950Z