References
- [Athreya and Chaika 12] J. S. Athreya and J. Chaika. “The Distribution of Gaps for Saddle Connection Directions.” Geom. Funct. Anal. 22: 6 (2012), 1491–1516.
- [Athreya 15] J. S. Athreya, J. Chaika, and S. Lelièvre. “The Gap Distribution of Slopes on the Golden L.” In Recent Trends in Ergodic Theory and Dynamical Systems, Contemporary Mathematics, vol. 631, pp. 47–62. Providence, RI: American Mathematical Society, 2015.
- [Augustin et al. 01] V. Augustin, F. P. Boca, C. Cobeli, and A. Zaharescu. “The h-Spacing Distribution between Farey Points.” Math. Proc. Camb. Philos. Soc. 131: 1 (2001), 23–38.
- [Boca 01] F. P. Boca, C. Cobeli, and A. Zaharescu. “A Conjecture of R. R. Hall on Farey Points.” J. R. Angew. Math. 535 (2001), 207–236.
- [Boca et al. 14] F. P. Boca, A. A. Popa, and A. Zaharescu. “Pair Correlation of Hyperbolic Lattice Angles.” Int. J. Number Theory 10: 8 (2014), 1955–1989.
- [Boca and Zaharescu 06] F. P. Boca and A. Zaharescu. “On the Correlations of Directions in the Euclidean Plane.” Trans. Am. Math. Soc. 358: 4 (2006), 1797–1825.
- [Bourgain and Fuchs 12] J. Bourgain and E. Fuchs. “A Proof of the Positive Density Conjecture for Integer Apollonian Circle Packings.” J. Am. Math. Soc. 24: 4 (2011), 945–967.
- [El-Baz et al. 15] D. El-Baz, J. Marklof, and I. Vinogradov. “The Distribution of Directions in an Affine Lattice: Two-Point Correlations and Mixed Moments.” Int. Math. Res. Not. 2015: 5 (2015), 1371–1400.
- [Elkies and McMullen 04] N. D. Elkies and C. T. McMullen. “Gaps in nmod1 and Ergodic Theory.” Duke Math. J. 123: 1 (2004), 95–139.
- [Fuchs 10] E. Fuchs. “Arithmetic Properties of Apollonian Circle Packings.” PhD diss., Princeton University, 2010.
- L. Gardi. “The Mandelbrot Set and the Fractal Nature of Light, the Universe, and Everything.” Paper presented at the SPIE Optical Engineering + Applications Conference, pp. 883210–883210, 2013.
- [Graham et al. 03] R. L. Graham, J. C. Lagarias, C. L. Mallows, A. R. Wilks, and C. H. Yan. “Apollonian Circle Packings: Number Theory.” J. Number Theory 100: 1 (2003), 1–45.
- [Hall 70] R. R. Hall. “A Note on Farey Series.” J. Lond. Math. Soc. (2), 2:139–148, 1970.
- [Kelmer and Kontorovich 15] D. Kelmer and A. Kontorovich. “On the Pair Correlation Density for Hyperbolic Angles.” Duke Math. J. 164: 3 (2015), 473–509.
- [Kirkwood and Buff 51] F. P. Kirkwood and J. G. Buff. “The Statistical Mechanical Theory of Solutions. I.” J. Chem. Phys. 19: 6 (1951), 774–777.
- [Kontorovich and Oh 11] A. Kontorovich and H. Oh. “Apollonian Circle Packings and Closed Horospheres on Hyperbolic 3-Manifolds.” J. Am. Math. Soc. 24: 3 (2011), 603–648. With an appendix by Oh and Nimish Shah.
- [Lax and Phillips 82] P. D. Lax and R. S. Phillips. “The Asymptotic Distribution of Lattice Points in Euclidean and Non-Euclidean Spaces.” J. Funct. Anal. 46: 3 (1982), 280–350.
- [Marklof and Vinogradov 14] J. Marklof and I. Vinogradov. “Directions in Hyperbolic Lattices.” Journal für die reine und angewandte Mathematik (Crelles Journal). Preprint, 2014.
- [McMullen 98] C. T. McMullen. “Hausdorff Dimension and Conformal Dynamics. III. Computation of Dimension.” Am. J. Math. 120: 4 (1998), 691–721.
- [Montgomery 73] H. L. Montgomery. “The Pair Correlation of Zeros of the Zeta Function.” Proc. Symp. Pure Math. 24 (1973) 181–193.
- [Oh and Shah 12] H. Oh and N. Shah. “The Asymptotic Distribution of Circles in the Orbits of Kleinian Groups.” Invent. Math. 187: 1 (2012), 1–35.
- [Risager and Södergren 14] M. S. Risager and A. Södergren. “Angles in Hyperbolic Lattices : The Pair Correlation Density.” Transactions of the American Mathematical Society. 369: 4 (2017), 2807–2841. Preprint.
- [Rudnick and Zhang 15] Z. Rudnick and X. Zhang. “Gap Distributions in Circle Packings.” Münster J. of Math. 10 (2017), 131–170. Submitted. Preprint, arxiv:1509.02989.
- [Soddy 36] F. Soddy. “The Kiss Precise.” Nature 137 (1936), 1021.
- [Uyanik and Work 16] C. Uyanik and G. Work. “The Distribution of Gaps for Saddle Connections on the Octagon.” Int. Math. Res. Not. 18 (2016), 5569–5602.
- [Zhang 15] X. Zhang. “The Gap Distribution of Directions in Some Schottky Groups.” Journal of Modern Dynamics. 11 (2017), 477–499. Preprint, 2015.