Ambient Prime Geodesic Theorems on Hyperbolic 3-Manifolds

被引：3

作者：

Dever, Lindsay ^{[1
]}

Milicevic, Djordje ^{[1
,2
]}

机构：

[1] Bryn Mawr Coll, Dept Math, 101 North Mer Ave, Bryn Mawr, PA 19010 USA

[2] Max Planck Inst Math, Vivatsgasse 7, D-53111 Bonn, Germany

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2023年 / 2023卷 / 01期

基金：

美国国家科学基金会;

关键词：

CLOSED GEODESICS; COMMENSURABILITY; HOLONOMY;

D O I：

10.1093/imrn/rnab048

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：588 / 635

页数：48

共 50 条

[21] The length spectra of arithmetic hyperbolic 3-manifolds and their totally geodesic surfaces
Linowitz, Benjamin
Meyer, Jeffrey S.
Pollack, Paul
NEW YORK JOURNAL OF MATHEMATICS, 2015, 21 : 955 - 972
[22] Homotopy hyperbolic 3-manifolds are hyperbolic
Gabai, D
Meyerhoff, GR
Thurston, N
ANNALS OF MATHEMATICS, 2003, 157 (02) : 335 - 431
[23] On the growth of the number of primitive totally geodesic surfaces in some hyperbolic 3-manifolds
Jung, Junehyuk
JOURNAL OF NUMBER THEORY, 2019, 202 : 160 - 175
[24] Arithmeticity of hyperbolic 3-manifolds containing infinitely many totally geodesic surfaces
Mohammadi, Amir
Margulis, Gregorii
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2022, 42 (03) : 1188 - 1219
[25] Geodesic foliations in Lorentz 3-manifolds
Zeghib, A
COMMENTARII MATHEMATICI HELVETICI, 1999, 74 (01) : 1 - 21
[26] Macfarlane hyperbolic 3-manifolds
Quinn, Joseph A.
ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2018, 18 (03): : 1603 - 1632
[27] Tubes in hyperbolic 3-manifolds
Przeworski, A
TOPOLOGY AND ITS APPLICATIONS, 2003, 128 (2-3) : 103 - 122
[28] TOTALLY GEODESIC FOLIATIONS ON 3-MANIFOLDS
JOHNSON, DL
WHITT, LB
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1979, 76 (02) : 355 - 357
[29] Horocycles in hyperbolic 3-manifolds
McMullen, Curtis T.
Mohammadi, Amir
Oh, Hee
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2016, 26 (03) : 961 - 973
[30] Horocycles in hyperbolic 3-manifolds
Curtis T. McMullen
Amir Mohammadi
Hee Oh
Geometric and Functional Analysis, 2016, 26 : 961 - 973

← 1 2 3 4 5 →