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On the Local-Global Conjecture for integral Apollonian gaskets
classification
🧮 math.NT
keywords
apollonianintegralconjecturedensitygasketgasketslocal-globaladmissible
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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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