Apollonian coronas and a new Zeta function

2019/09/22 by Jerzy Kocik, Kocik, Jerzy · 2 citations
Mathematics · #Algebraic and Geometric Analysis #Mathematical Dynamics and Fractals #Mathematics and Applications #math.MG #msc:14C10 #msc:15A66 #msc:28A90 #msc:52C26

paper · pdf · doi:10.48550/arxiv.1909.09941

19 pages, 14 figures

arxiv created 2019/09/22 · arxiv updated 2019/09/24

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.

Citations

• Spinors and Descartes configurations of disks

Cited by

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

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