Apollonian coronas and a new Zeta function

Abstract

We find a formula for the area of disks tangent to a given disk in an Apollonian disk packing (corona) in terms of a certain novel arithmetic Zeta function. The idea is based on "tangency spinors" defined for pairs of tangent disks.

19 pages, 14 figures

References in corpus (2)

• A theorem on circle configurations
• Spinors and Descartes configurations of disks

Cited by in corpus (2)

• Spinors, lattices, and classification of integral Apollonian disk packings
• Integral spinors, Apollonian disk packings, and Descartes groups