On the Local-Global Conjecture for integral Apollonian gaskets

2012/05/20 by Bourgain, Jean, Kontorovich, Alex · 2 citations
#11D85 #11F41 #20H10 #22E40 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1205.4416

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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