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arXiv · 1205.4416

On the Local-Global Conjecture for integral Apollonian gaskets

Jean Bourgain·Alex Kontorovich
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Abstract

We prove that a set of density one satisfies the local-global conjecture for integral Apollonian gaskets. That is, for a fixed integral, primitive Apollonian gasket, almost every (in the sense of density) admissible (passing local obstructions) integer is the curvature of some circle in the gasket.

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Jean Bourgain, Alex Kontorovich. 2012-05-20. On the Local-Global Conjecture for integral Apollonian gaskets. https://arxiv.org/abs/1205.4416

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