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arXiv:1312.4650 [math.NT]AbstractReferencesReviewsResources

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

Xin Zhang

Published 2013-12-17, updated 2015-04-20Version 2

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.

Comments: 40 pages
Categories: math.NT, math.GR, math.SP
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