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

2013/12/17 by Xin Zhang, Zhang, Xin · 1 citation
Materials Science · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Quasicrystal Structures and Properties #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1312.4650

openalex publication_date 2013/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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