Sector Estimates for Hyperbolic Isometries

Jean Bourgain, Alex Kontorovich, Peter Sarnak

Type: Article

Publication Date: 2010-09-29

Citations: 55

DOI: https://doi.org/10.1007/s00039-010-0092-5

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.

Locations

Geometric and Functional Analysis - View
arXiv (Cornell University) - View - PDF
Geometric and Functional Analysis - View
arXiv (Cornell University) - View - PDF

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+ PDF	The limit set of a Fuchsian group	1976	S. J. Patterson
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+ PDF	Density of integer points on affine homogeneous varieties	1993	William Duke Zeév Rudnick Peter Sarnak
+ PDF	Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups	1984	Dennis Sullivan
+	Asymptotic properties of unitary representations	1979	Roger Howe Calvin C. Moore
+ PDF	Uniform expansion bounds for Cayley graphs of SL<sub>2</sub>(𝔽<sub>p</sub>)	2008	Jean Bourgain Alex Gamburd