Quantitative ergodic theorems and their number-theoretic applications
From MaRDI portal
Publication:5175015
DOI10.1090/S0273-0979-2014-01462-4zbMath1351.37039arXiv1304.6847MaRDI QIDQ5175015
Publication date: 19 February 2015
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1304.6847
Ergodic theory on groups (22D40) Semisimple Lie groups and their representations (22E46) Ergodic theorems, spectral theory, Markov operators (37A30) Metric theory (11J83) Representation-theoretic methods; automorphic representations over local and global fields (11F70) General groups of measure-preserving transformations and dynamical systems (37A15) Arithmetic dynamics on general algebraic varieties (37P55)
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Cites Work
- Random walks in Euclidean space
- Averages in the plane over convex curves and maximal operators
- Bounded orbits of flows on homogeneous spaces
- Local analysis of Selberg's trace formula
- On representations of integers in thin subgroups of \(\text{SL}_2(\mathbb Z)\)
- Integral points on quadrics in three variables whose coordinates have few prime factors
- Prime and almost prime integral points on principal homogeneous spaces
- Igusa integrals and volume asymptotics in analytic and adelic geometry
- Different approaches to the distribution of primes
- Pointwise ergodic theorems for radial averages on simple Lie groups. II
- Uniform distribution of orbits of lattices on spaces of frames
- A simple proof of some ergodic theorems
- Affine linear sieve, expanders, and sum-product
- Homogeneous asymptotic limits of Haar measures of semisimple linear groups and their lattices
- Distribution of lattice orbits on homogeneous varieties
- Rational approximation on spheres
- Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations and their fractal limits
- Pointwise ergodic theorems for arithmetic sets. With an appendix on return-time sequences, jointly with Harry Furstenberg, Yitzhak Katznelson and Donald S. Ornstein
- Rational points on the unit sphere
- Polynomial dynamic and lattice orbits in \(S\)-arithmetic homogeneous spaces
- Nichteuklidische Gitterpunktprobleme und Gleichverteilung in linearen algebraischen Gruppen
- The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces
- Non-Abelian harmonic analysis. Applications of \(SL(2,{\mathbb{R}})\)
- Ramanujan duals. II
- The resolvent of the Laplacian on locally symmetric spaces
- The Kunze-Stein phenomenon
- Counterexamples in ergodic theory and number theory
- Asymptotic properties of unitary representations
- Spectral transfer and pointwise ergodic theorems for semi-simple Kazhdan groups
- Flows on homogeneous spaces and Diophantine approximation on manifolds
- Density of integer points on affine homogeneous varieties
- Mixing, counting, and equidistribution in Lie groups
- Ergodic averages on spheres
- Discrete groups, expanding graphs and invariant measures. Appendix by Jonathan D. Rogawski
- A generalization of Birkhoff's pointwise ergodic theorem
- Pointwise ergodic theorems for radial averages on simple Lie groups. I
- Analogs of Wiener's ergodic theorems for semisimple groups. I
- Pointwise ergodic theorems for radial averages on the Heisenberg group
- Démonstration de la conjecture \(\tau\). (Proof of the \(\tau\)-conjecture.)
- Rational points on the sphere
- Analogs of Wiener's ergodic theorems for semisimple Lie groups. II
- Pointwise theorems for amenable groups.
- Best possible rates of distribution of dense lattice orbits in homogeneous spaces
- Logarithm laws for flows on homogeneous spaces
- Group structure and the pointwise ergodic theorem for connected amenable groups
- Uniform pointwise bounds for matrix coefficients of unitary representations and applications to Kazhdan constants
- Diophantine approximation for negatively curved manifolds
- Orbit distribution on \(\mathbb R^2\) under the natural action of \(\mathrm{SL}(2,\mathbb Z)\)
- Ergodic properties of linear actions of \((2\times 2)\)-matrices
- On Selberg's eigenvalue conjecture
- Ergodic averages on circles
- Unipotent flows and counting lattice points on homogeneous varieties
- Effective equidistribution of \(S\)-integral points on symmetric varieties
- Expansion in perfect groups.
- Badly approximable systems of affine forms
- Resolvent and lattice points on symmetric spaces of strictly negative curvature
- Flows on homogeneous spaces and Diophantine properties of matrices.
- Apollonian circle packings: dynamics and number theory
- The hyperbolic lattice point count in infinite volume with applications to sieves
- Lattice actions on the plane revisited
- Ergodic theory and the duality principle on homogeneous spaces
- Sieving and expanders
- Connection of the dual space of a group with the structure of its closed subgroups
- Automorphic forms on GL (2)
- Proximality and equidistribution on the Furstenberg boundary
- Über eine neue Klasse automorpher Funktionen und ein Gitterpunktproblem in der hyperbolischen Ebene. I
- Hausdorff dimension of diophantine geodesics in negatively curved manifolds
- Harmonic analysis, Ergodic theory and Counting for thin groups
- Almost prime Pythagorean triples in thin orbits
- Metric Diophantine approximation on homogeneous varieties
- New Lattice Point Asymptotics for Products of Upper Half-planes
- Apollonian circle packings and closed horospheres on hyperbolic 3-manifolds
- Stationary measures and equidistribution for orbits of nonabelian semigroups on the torus
- Expander graphs in pure and applied mathematics
- Counting lattice points
- Integral Apollonian Packings
- A proof of the positive density conjecture for integer Apollonian circle packings
- Producing Prime Numbers via Sieve Methods
- Lattice orbit distribution on ℝ2
- The Ergodic Theory of Lattice Subgroups (AM-172)
- Divergent trajectories of flows on homogeneous spaces and Diophantine approximation.
- Hecke operators and distributing points on the sphere I
- Hecke operators and distributing points on S2. II
- Amenability, Kazhdan's property T, strong ergodicity and invariant means for ergodic group-actions
- A lattice‐point problem in hyperbolic space
- Problems in harmonic analysis related to curvature
- A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
- Tempered subgroups and representations with minimal decay of matrix coefficients
- Distribution des orbites des réseaux sur le plan réel
- Density measure of rational points on Abelian varieties
- Subanalytic Functions
- Harmonic Analysis and Pointwise Ergodic Theorems for Noncommuting Transformations
- Spectra of hyperbolic surfaces
- Lattice action on the boundary of SL $(n,\mathbb{R})}$
- Proof of the Quasi-Ergodic Hypothesis
- A Symbolic Proof of a Theorem of Margulis on Geodesic Arcs on Negatively Curved Manifolds
- Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
- Diophantine equations and ergodic theorems
- On Arnol’d’s and Kazhdan’s equidistribution problems
- Lifting, restricting and sifting integral points on affine homogeneous varieties
- From Apollonius to Zaremba: Local-global phenomena in thin orbits
- The role of the Ramanujan conjecture in analytic number theory
- Diophantine Approximation and Automorphic Spectrum
- The affine sieve
- Report on Diophantine approximations
- Uniformly Bounded Representations and Harmonic Analysis of the 2 x 2 Real Unimodular Group
- ON THE MAXIMAL ERGODIC THEOREM
- On the existence and irreducibility of certain series of representations
- Some Mean Ergodic Theorems
- Almost-primes represented by quadratic polynomials
- Hypersurfaces with constant scalar curvature in space forms
- A general ergodic theorem
- Uniform estimates for spherical functions on complex semisimple Lie groups
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