Some Experiments with Integral Apollonian Circle Packings

DOI10.1080/10586458.2011.565255zbMath1259.11065arXiv1001.1406OpenAlexW2594307166MaRDI QIDQ4915401

Katherine Sanden, Elena Fuchs

Publication date: 10 April 2013

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.1406

zbMATH Keywords

Diophantine equationscomputational number theoryintegral Apollonian circle packings

Mathematics Subject Classification ID

Lattice packing and covering (number-theoretic aspects) (11H31) Evaluation of number-theoretic constants (11Y60) Circle packings and discrete conformal geometry (52C26)

Related Items (15)

A proof of the positive density conjecture for integer Apollonian circle packings ⋮ Integral Apollonian circle packings and prime curvatures ⋮ The Apollonian structure of Bianchi groups ⋮ On representations of integers in thin subgroups of \(\text{SL}_2(\mathbb Z)\) ⋮ Generalization of Selberg's \(\frac {3}{16} \) theorem and affine sieve ⋮ Strong approximation in the Apollonian group ⋮ Local-global principles in circle packings ⋮ On the local-global conjecture for integral Apollonian gaskets. With an appendix by Péter P. Varjú ⋮ From Apollonius to Zaremba: Local-global phenomena in thin orbits ⋮ Counting problems in Apollonian packings ⋮ Apollonian circle packings: dynamics and number theory ⋮ Recursive sequences in the Ford sphere packing ⋮ The local-global principle for integral Soddy sphere packings ⋮ Quaternion orders and sphere packings ⋮ Expander graphs in pure and applied mathematics

Cites Work

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• Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids
• Strong approximation in the Apollonian group
• Affine linear sieve, expanders, and sum-product
• Apollonian circle packings: Number theory
• Apollonian circle packings and closed horospheres on hyperbolic 3-manifolds
• Integral Apollonian Packings
• A proof of the positive density conjecture for integer Apollonian circle packings
• The Apollonian Packing of Circles

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