Effective Bisector Estimate with Application to Apollonian Circle Packings

DOI10.1093/imrn/rnt037zbMath1296.11088arXiv1204.5498OpenAlexW2593008947MaRDI QIDQ2878727

Ilya Vinogradov

Publication date: 5 September 2014

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.5498

zbMATH Keywords

critical exponentdiscrete subgroupApollonian circle packingbisector estimate

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Lattice packing and covering (number-theoretic aspects) (11H31) Circle packings and discrete conformal geometry (52C26)

Related Items (13)

Closed geodesics and holonomies for Kleinian manifolds ⋮ On the rate of equidistribution of expanding horospheres in finite-volume quotients of \(\mathrm{SL}(2,\mathbb{C})\) ⋮ Effective equidistribution of circles in the limit sets of Kleinian groups ⋮ Effective circle count for Apollonian packings and closed horospheres ⋮ Apollonian packings and Kac-Moody root systems ⋮ On the local-global principle for integral Apollonian 3-circle packings ⋮ 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 ⋮ Uniform exponential mixing and resonance free regions for convex cocompact congruence subgroups of $\operatorname {SL}_2(\mathbb {Z})$ ⋮ Apollonian circle packings: dynamics and number theory ⋮ Spectral gap and exponential mixing on geometrically finite hyperbolic manifolds

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