English

Ambient prime geodesic theorems on hyperbolic 3-manifolds

Number Theory 2022-06-23 v3 Differential Geometry

Abstract

We prove prime geodesic theorems counting primitive closed geodesics on a compact hyperbolic 3-manifold with length and holonomy in prescribed intervals, which are allowed to shrink. Our results imply effective equidistribution of holonomy and have both the rate of shrinking and the strength of the error term fully symmetric in length and holonomy.

Keywords

Cite

@article{arxiv.2004.11774,
  title  = {Ambient prime geodesic theorems on hyperbolic 3-manifolds},
  author = {Lindsay Dever and Djordje Milićević},
  journal= {arXiv preprint arXiv:2004.11774},
  year   = {2022}
}

Comments

39 pages, final version, IMRN

R2 v1 2026-06-23T15:04:42.853Z