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Integral Apollonian circle packings and prime curvatures

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Journal d'Analyse Mathématique Aims and scope

An Erratum to this article was published on 29 August 2013

Abstract

It is shown that any primitive integral Apollonian circle packing captures a fraction of the prime numbers. Basically, the method consists of applying the circle method and considering the curvatures produced by a well-chosen family of binary quadratic forms.

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Authors and Affiliations

  1. Institute for Advanced Study, Princeton, NJ, 08540, USA

    J. Bourgain

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  1. J. Bourgain
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Correspondence to J. Bourgain.

Additional information

The author was partially supported by NSF grants DMS-0808042 and DMS-0835373.

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Bourgain, J. Integral Apollonian circle packings and prime curvatures. JAMA 118, 221–249 (2012). https://doi.org/10.1007/s11854-012-0034-2

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  • DOI: https://doi.org/10.1007/s11854-012-0034-2

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