Sector estimates for hyperbolic isometries

DOI10.1007/s00039-010-0092-5zbMath1208.22007arXiv1001.4541OpenAlexW2962994636WikidataQ105987202 ScholiaQ105987202MaRDI QIDQ607665

Jean Bourgain, Peter C. Sarnak, Alex V. Kontorovich

Publication date: 3 December 2010

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.4541

zbMATH Keywords

Fuchsian groupsinfinite volumeHyperbolic lattice point countingsector estimates

Mathematics Subject Classification ID

Homogeneous spaces (22F30) Ergodicity, mixing, rates of mixing (37A25) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Homogeneous flows (37A17)

Related Items

Closed geodesics and holonomies for Kleinian manifolds, On Trace Sets of Restricted Continued Fraction Semigroups, The gap distribution of directions in some Schottky groups, Effective circle count for Apollonian packings and closed horospheres, Pair correlation of hyperbolic lattice angles, Almost prime coordinates for anisotropic and thin Pythagorean orbits, On Zaremba's conjecture, Effective equidistribution of shears and applications, On the local-global conjecture for integral Apollonian gaskets. With an appendix by Péter P. Varjú, On Zaremba's conjecture, From Apollonius to Zaremba: Local-global phenomena in thin orbits, Uniform exponential mixing and resonance free regions for convex cocompact congruence subgroups of $\operatorname {SL}_2(\mathbb {Z})$, Directions in orbits of geometrically finite hyperbolic subgroups, Spectral gap and exponential mixing on geometrically finite hyperbolic manifolds, On the hyperbolic orbital counting problem in conjugacy classes, Matrix coefficients, counting and primes for orbits of geometrically finite groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Generalization of Selberg's \(\frac {3}{16} \) theorem and affine sieve
• Asymptotic behavior of matrix coefficients of admissible representations
• Local analysis of Selberg's trace formula
• Sparse equidistribution problems, period bounds and subconvexity
• On the spectral gap for infinite index ``congruence subgroups of \(SL_2(\mathbb{Z})\)
• Expansion and random walks in \(\text{SL}_d(\mathbb{Z}/p^n\mathbb{Z})\). I.
• Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups
• The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces
• The limit set of a Fuchsian group
• Asymptotic properties of unitary representations
• Density of integer points on affine homogeneous varieties
• Mixing, counting, and equidistribution in Lie groups
• The hyperbolic lattice point count in infinite volume with applications to sieves
• Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\).
• Almost prime Pythagorean triples in thin orbits
• Equidistribution and counting for orbits of geometrically finite hyperbolic groups