scholarly journals The Erdős-Kac theorem for curvatures in integral apollonian circle packings

2011 ◽  
Vol 89 (103) ◽  
pp. 11-17
Author(s):  
Goran Djankovic
Keyword(s):  
Type Result ◽  
Circle Packings ◽  
Apollonian Circle Packings

The Erd?s-Kac type result for curvatures of circles in integral Apollonian packings is proved.

scholarly journals Apollonian circle packings: Number theory II. Spherical and hyperbolic packings

2007 ◽  
Vol 14 (3) ◽  
pp. 437-469 ◽  
Author(s):  
Nicholas Eriksson ◽  
Jeffrey C. Lagarias
Keyword(s):  
Number Theory ◽  
Circle Packings ◽  
Apollonian Circle Packings

scholarly journals On integral Apollonian circle packings

2006 ◽  
Vol 119 (2) ◽  
pp. 171-193 ◽  
Author(s):  
S. Northshield
Keyword(s):  
Circle Packings ◽  
Apollonian Circle Packings

scholarly journals Apollonian Circle Packings: Geometry and Group Theory III. Higher Dimensions

2005 ◽  
Vol 35 (1) ◽  
pp. 37-72 ◽  
Author(s):  
Ronald L. Graham ◽  
Jeffrey C. Lagarias ◽  
Colin L. Mallows ◽  
Allan R. Wilks ◽  
Catherine H. Yan
Keyword(s):  
Group Theory ◽  
Higher Dimensions ◽  
Circle Packings ◽  
Apollonian Circle Packings

scholarly journals Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings

2005 ◽  
Vol 35 (1) ◽  
pp. 1-36 ◽  
Author(s):  
Ronald L. Graham ◽  
Jeffrey C. Lagarias ◽  
Colin L. Mallows ◽  
Allan R. Wilks ◽  
Catherine H. Yan
Keyword(s):  
Group Theory ◽  
Circle Packings ◽  
Apollonian Circle Packings

scholarly journals On the local-global principle for integral Apollonian 3-circle packings

2018 ◽  
Vol 2018 (737) ◽  
pp. 71-110 ◽  
Author(s):  
Xin Zhang
Keyword(s):  
Symmetry Group ◽  
Spectral Gap ◽  
Reduction Theory ◽  
Circle Packings ◽  
Apollonian Circle Packings ◽  
Global Principle ◽  
The Way

AbstractIn this paper we study the integral properties of Apollonian 3-circle packings, which are variants of the standard Apollonian circle packings. Specifically, we study the reduction theory, formulate a local-global conjecture, and prove a density one version of this conjecture. Along the way, we prove a uniform spectral gap for the congruence towers of the symmetry group.

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