Sector estimates for hyperbolic isometries
Jean Bourgain, Alex Kontorovich, and Peter Sarnak
TL;DR
This paper establishes orbital counting estimates for Fuchsian groups of the second kind, which are crucial for applications like producing primes via the Affine Linear Sieve.
Contribution
It provides new orbital counting results for hyperbolic isometries of Fuchsian groups, advancing understanding in geometric group theory and number theory.
Findings
Proved orbital counting estimates for Fuchsian groups of the second kind
Applied these results to prime production in the Affine Linear Sieve
Enhanced methods for analyzing 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 [BourgainKontorovich2009] to produce primes in the Affine Linear Sieve.
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