From Apollonius to Zaremba: Local-global phenomena in thin orbits (Q4918438)

scientific article; zbMATH DE number 6157470

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English	From Apollonius to Zaremba: Local-global phenomena in thin orbits	scientific article; zbMATH DE number 6157470

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instance of

scholarly article

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title

From Apollonius to Zaremba: Local-global phenomena in thin orbits (English)

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published in

Bulletin of the American Mathematical Society

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publication date

25 April 2013

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full work available at URL

https://arxiv.org/abs/1208.5460

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author

Alex V. Kontorovich

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describes a project that uses

OEIS

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MaRDI profile type

MaRDI publication profile

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cites work

A proof of the positive density conjecture for integer Apollonian circle packings

0 references

Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\).

0 references

Sieving and expanders

0 references

Affine linear sieve, expanders, and sum-product

0 references

Generalization of Selberg's \(\frac {3}{16} \) theorem and affine sieve

0 references

Approximate subgroups of linear groups.

0 references

On representations of integers in thin subgroups of \(\text{SL}_2(\mathbb Z)\)

0 references

On Zaremba's conjecture

0 references

On the local-global conjecture for integral Apollonian gaskets. With an appendix by Péter P. Varjú

0 references

Sector estimates for hyperbolic isometries

0 references

A sum-product estimate in finite fields, and applications

0 references

The sum-product theorem in \(\mathbb Z_q\) with \(q\) arbitrary

0 references

The residual set dimension of the Apollonian packing

0 references

The Sequence of Radii of the Apollonian Packing

0 references

Expansion in \(\text{SL}_d(\mathbb Z/q\mathbb Z)\), \(q\) arbitrary.

0 references

Q4177654

0 references

The Problem of Apollonius

0 references

On decay of correlations in Anosov flows

0 references

Density of integer points on affine homogeneous varieties

0 references

Q4787524

0 references

Apollonian circle packings: number theory. II: Spherical and hyperbolic packings

0 references

Mixing, counting, and equidistribution in Lie groups

0 references

Some Experiments with Integral Apollonian Circle Packings

0 references

Strong approximation in the Apollonian group

0 references

On the spectral gap for infinite index ``congruence'' subgroups of SL\(_2(\mathbb{Z})\)

0 references

Apollonian circle packings: Number theory

0 references

Apollonian circle packings: Geometry and group theory. III: Higher dimensions

0 references

Harald Cramér and the distribution of prime numbers

0 references

Growth and generation in \(\text{SL}_2(\mathbb{Z}/p\mathbb{Z})\).

0 references

Continued fraction Cantor sets, Hausdorff dimension, and functional analysis

0 references

A polynomial time algorithm for the Hausdorff dimension of continued fraction Cantor sets

0 references

Computing the dimension of dynamically defined sets: E_2 and bounded continued fractions

0 references

Apollonian circle packings and closed horospheres on hyperbolic 3-manifolds

0 references

Almost prime Pythagorean triples in thin orbits

0 references

The hyperbolic lattice point count in infinite volume with applications to sieves

0 references

Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations and their fractal limits

0 references

Beyond the Descartes Circle Theorem

0 references

Effective circle count for Apollonian packings and closed horospheres

0 references

The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces

0 references

Expander graphs in pure and applied mathematics

0 references

Some Fundamental Geometrical Properties of Plane Sets of Fractional Dimensions

0 references

Hausdorff dimension and conformal dynamics, III: Computation of dimension

0 references

Congruence Properties of Zariski-Dense Subgroups I

0 references

Expanding maps on Cantor sets and analytic continuation of zeta functions

0 references

Quasi-Monte Carlo methods and pseudo-random numbers

0 references

Dynamics on geometrically finite hyperbolic manifolds with applications to Apollonian circle packings and beyond

0 references

The asymptotic distribution of circles in the orbits of Kleinian groups

0 references

The limit set of a Fuchsian group

0 references

Q4826727

0 references

Q5324217

0 references

Integral Apollonian Packings

0 references

Irregularities of distribution, VII

0 references

Counting lattices in simple Lie groups: the positive characteristic case

0 references

The affine sieve

0 references

The Bowl of Integers and the Hexlet

0 references

Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups

0 references

Bounds for multiplicities of automorphic representations

0 references

Effective Bisector Estimate with Application to Apollonian Circle Packings

0 references

Good lattic points, discrepancy, and numerical integration

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Identifiers

zbMATH Open document ID

1309.11040

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DOI

10.1090/S0273-0979-2013-01402-2

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:4918438