English

The Prime Geodesic Theorem

Number Theory 2014-05-22 v1

Abstract

We study the distribution of closed geodesics for the modular surface. We improve the error term in the prime geodesic theorem, and obtain results on prime geodesics in very short intervals conditionally on the generalized Riemann Hypothesis for Dirichlet L-functions. We emphasize a connection between the closed geodesics and certain Dirichlet L-functions.

Keywords

Cite

@article{arxiv.1011.5486,
  title  = {The Prime Geodesic Theorem},
  author = {K. Soundararajan and Matthew P. Young},
  journal= {arXiv preprint arXiv:1011.5486},
  year   = {2014}
}

Comments

13 pages

R2 v1 2026-06-21T16:48:41.256Z