Integral Apollonian Packings

@article{Sarnak2011IntegralAP,
  title={Integral Apollonian Packings},
  author={P. Sarnak},
  journal={The American Mathematical Monthly},
  year={2011},
  volume={118},
  pages={291 - 306}
}
  • P. Sarnak
  • Published 2011
  • Mathematics, Computer Science
  • The American Mathematical Monthly
    • Abstract We review the construction of integral Apollonian circle packings. There are a number of Diophantine problems that arise in the context of such packings. We discuss some of them and describe some recent advances. 
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        References

        SHOWING 1-10 OF 40 REFERENCES
        ON SUMS OF THREE SQUARES
        • 23
        • PDF
        Arithmetic Properties of Apollonian Circle Packings
        • 16
        • Highly Influential
        • PDF
        Apollonian Circle Packings
        • 6
        • Highly Influential
        • PDF
        Apollonian circle packings:number theory
        • 128
        • PDF
        The sequence of radii of the Apollonian packing
        • 53
        • PDF
        Affine linear sieve, expanders, and sum-product
        • 152
        • PDF
        An infinite packing theorem for spheres
        • 12
        • PDF
        Sums of three squares
        • 17
        • PDF
        Congruence Properties of Zariski‐Dense Subgroups I
        • 111
        • PDF
        Rational Quadratic Forms
        • 175