3 papers
math.NT2022
On Length Sets of Subarithmetic Hyperbolic Manifolds
Alex Kontorovich, Xin Zhang
We formulate the Asymptotic Length-Saturation Conjecture on the length sets of closed geodesics on hyperbolic manifolds whose fundamental groups are subarithmetic, that is, contain…
math.DS2017
Statistical Regularity of Apollonian Gaskets
Xin Zhang
Apollonian gaskets are formed by repeatedly filling the gaps between three mutually tangent circles with further tangent circles. In this paper we give explicit formulas for the th…
math.MG2017
Spatial Statistics of Apollonian Gaskets
Weiru Chen, Mo Jiao, Calvin Kessler +2
Apollonian gaskets are formed by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We experimentally study the pair correlation…