On the Local-Global Principle for Integral Apollonian-3 Circle Packings

Abstract

In 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 congruence towers of the symmetry group.

40 pages

References in corpus (2)

• Counting, Mixing and Equidistribution of horospheres in geometrically finite rank one locally symmetric manifolds
• Higher-order Statistics of Weak Lensing Shear and Flexion

Cited by in corpus (1)

• Geometry and Arithmetic of Crystallographic Sphere Packings