Ambient Prime Geodesic Theorems on Hyperbolic 3-Manifolds-Reference-Cited by-同舟云学术

Ambient Prime Geodesic Theorems on Hyperbolic 3-Manifolds

Published:2021-10-05 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Dever Lindsay¹,Milićević Djordje¹²

Affiliation:

1. Bryn Mawr College, Department of Mathematics, 101 North Merion Avenue, Bryn Mawr, PA 19010, USA

2. Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germany

Abstract

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.

Funder

National Science Foundation

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnab048/40509269/rnab048.pdf

Reference28 articles.

1. Prime geodesic theorem in the 3-dimensional hyperbolic space;Balkanova;Trans. Amer. Math. Soc.,2019

2. Prime geodesic theorem for the Picard manifold;Balkanova;Adv. Math.,2020

3. Bykovskii-type theorem for the Picard manifold;Balog;Internat. Math. Res. Notices,2020

4. Counting cusp forms by analytic conductor;Brumley;arXiv e-prints,2018

5. Geodesics and commensurability classes of arithmetic hyperbolic 3-manifolds;Chinburg;Duke Math. J.,2008

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. The Prime Geodesic Theorem in Arithmetic Progressions;International Mathematics Research Notices;2024-09-12

2. Bias in the distribution of holonomy on compact hyperbolic 3-manifolds;Mathematische Annalen;2024-06-06

3. Beyond the spherical sup-norm problem;Journal de Mathématiques Pures et Appliquées;2022-12