On Length Sets of Subarithmetic Hyperbolic Manifolds
Number Theory
2022-01-27 v1 Group Theory
Abstract
We formulate the Asymptotic Length-Saturation Conjecture on the length sets of closed geodesics on hyperbolic manifolds whose fundamental groups are subarithmetic, that is, contained in an arithmetic group. We prove the first instance of the conjecture for punctured, Zariski dense covers of the modular surface. The tools involved include the Orbital Circle Method, expansion and counting in congruence towers of thin groups, estimates for exponential sums, bilinear forms, and quadratic L-series.
Cite
@article{arxiv.2201.10955,
title = {On Length Sets of Subarithmetic Hyperbolic Manifolds},
author = {Alex Kontorovich and Xin Zhang},
journal= {arXiv preprint arXiv:2201.10955},
year = {2022}
}
Comments
68 pages, 1 figure