Sector Estimates for Hyperbolic Isometries

Jean Bourgain; Alex Kontorovich; Peter Sarnak

doi:10.1007/s00039-010-0092-5

Sector Estimates for Hyperbolic Isometries

Jean Bourgain
, Alex Kontorovich
, Peter Sarnak

Mathematics

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

We prove various orbital counting statements for Fuchsian groups of the second kind. These are of independent interest, and also are used in the companion paper [BK] to produce primes in the Affine Linear Sieve.

Original language	English (US)
Pages (from-to)	1175-1200
Number of pages	26
Journal	Geometric and Functional Analysis
Volume	20
Issue number	5
DOIs	https://doi.org/10.1007/s00039-010-0092-5
State	Published - Nov 2010

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

Keywords

Fuchsian groups
Hyperbolic lattice point counting
infinite volume
sector estimates

Access to Document

10.1007/s00039-010-0092-5

Cite this

@article{835c31bd0fa54aab8221d99d158d70c8,

title = "Sector Estimates for Hyperbolic Isometries",

abstract = "We prove various orbital counting statements for Fuchsian groups of the second kind. These are of independent interest, and also are used in the companion paper [BK] to produce primes in the Affine Linear Sieve.",

keywords = "Fuchsian groups, Hyperbolic lattice point counting, infinite volume, sector estimates",

author = "Jean Bourgain and Alex Kontorovich and Peter Sarnak",

note = "Funding Information: Keywords and phrases: Hyperbolic lattice point counting, Fuchsian groups, infinite volume, sector estimates 2010 Mathematics Subject Classification: 22E45, 22F30, 37A17, 37A25 Bourgain is partially supported by NSF grant DMS-0808042. Kontorovich is partially supported by NSF grants DMS-0802998 and DMS-0635607, and the Ellentuck Fund at IAS. Sarnak is partially supported by NSF grant DMS-0758299.",

year = "2010",

month = nov,

doi = "10.1007/s00039-010-0092-5",

language = "English (US)",

volume = "20",

pages = "1175--1200",

journal = "Geometric and Functional Analysis",

issn = "1016-443X",

publisher = "Springer International Publishing",

number = "5",

}

TY - JOUR

T1 - Sector Estimates for Hyperbolic Isometries

AU - Bourgain, Jean

AU - Kontorovich, Alex

AU - Sarnak, Peter

N1 - Funding Information: Keywords and phrases: Hyperbolic lattice point counting, Fuchsian groups, infinite volume, sector estimates 2010 Mathematics Subject Classification: 22E45, 22F30, 37A17, 37A25 Bourgain is partially supported by NSF grant DMS-0808042. Kontorovich is partially supported by NSF grants DMS-0802998 and DMS-0635607, and the Ellentuck Fund at IAS. Sarnak is partially supported by NSF grant DMS-0758299.

PY - 2010/11

Y1 - 2010/11

N2 - We prove various orbital counting statements for Fuchsian groups of the second kind. These are of independent interest, and also are used in the companion paper [BK] to produce primes in the Affine Linear Sieve.

AB - We prove various orbital counting statements for Fuchsian groups of the second kind. These are of independent interest, and also are used in the companion paper [BK] to produce primes in the Affine Linear Sieve.

KW - Fuchsian groups

KW - Hyperbolic lattice point counting

KW - infinite volume

KW - sector estimates

UR - https://www.scopus.com/pages/publications/78649276989

UR - https://www.scopus.com/pages/publications/78649276989#tab=citedBy

U2 - 10.1007/s00039-010-0092-5

DO - 10.1007/s00039-010-0092-5

M3 - Article

AN - SCOPUS:78649276989

SN - 1016-443X

VL - 20

SP - 1175

EP - 1200

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 5

ER -

Sector Estimates for Hyperbolic Isometries

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this