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math.NT2024
Prime and thickened prime components in Apollonian circle packings
Holley Friedlander, Elena Fuchs, Piper Harris +5
Inspired by a question of Sarnak, we introduce the notion of a prime component in an Apollonian circle packing: a maximal tangency-connected subset having all prime curvatures. We…
math.NT2010
Some experiments with integral Apollonian circle packings
Elena Fuchs, Katherine Sanden
Bounded Apollonian circle packings (ACP's) are constructed by repeatedly inscribing circles into the triangular interstices of a configuration of four mutually tangent circles, one…