Integral Apollonian circle packings and prime curvatures

Details Integral Apollonian circle packings and prime curvatures Integral Apollonian circle packings and prime curvatures

2011-05-25

arxiv.org/abs/1105.5127v3

Mathematics

Number Theory

26 pages

Scientific paper

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

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