@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 = "Birkhauser Verlag Basel",
number = "5",
}