Integral Apollonian circle packings and prime curvatures

DOI10.1007/s11854-012-0034-2zbMath1281.52011arXiv1105.5127OpenAlexW1990547060MaRDI QIDQ351307

Jean Bourgain

Publication date: 11 July 2013

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.5127

zbMATH Keywords

Gauss sumbinary quadratic forms(integral) Apollonian circle packingDescartes quadratic form

Mathematics Subject Classification ID

Packing and covering in (2) dimensions (aspects of discrete geometry) (52C15) Quadratic forms (reduction theory, extreme forms, etc.) (11H55)

Related Items (6)

On Trace Sets of Restricted Continued Fraction Semigroups ⋮ On the local-global conjecture for integral Apollonian gaskets. With an appendix by Péter P. Varjú ⋮ Counting problems in Apollonian packings ⋮ Apollonian circle packings: dynamics and number theory ⋮ Recursive sequences in the Ford sphere packing ⋮ Levels of distribution and the affine sieve

Cites Work

• Generalization of Selberg's \(\frac {3}{16} \) theorem and affine sieve
• On \(\Lambda\) (p)-subsets of squares
• On representations of integers in thin subgroups of \(\text{SL}_2(\mathbb Z)\)
• Roth's theorem in the primes
• Apollonian circle packings: Number theory
• On the local-global conjecture for integral Apollonian gaskets. With an appendix by Péter P. Varjú
• Apollonian circle packings and closed horospheres on hyperbolic 3-manifolds
• A proof of the positive density conjecture for integer Apollonian circle packings
• On Representation of Integers by Binary Quadratic Forms
• Some Experiments with Integral Apollonian Circle Packings

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