13 citations · 20 across the 8 of their papers we have counts for
8 papers
Sum-product phenomenon in quotients of rings of algebraic integers
Jincheng Tang, Xin Zhang
We obtain a bounded generation theorem over , where is the ring of integers of a number field and a general ideal of …
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…
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…
Local-global principles in circle packings
Elena Fuchs, Katherine E. Stange, Xin Zhang
We generalize work of Bourgain-Kontorovich and Zhang, proving an almost local-to-global property for the curvatures of certain circle packings, to a large class of Kleinian groups.…
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…
The gap distribution of directions in some Schottky groups
Xin Zhang
We prove the existence and some properties of the limiting gap distribution functions for the directions of orbits of some infinite covolume subgroups of in th…
Gap Distributions in Circle Packings
Zeev Rudnick, Xin Zhang
We determine the distribution of nearest neighbour spacings between the tangencies to a fixed circle in a class of circle packings generated by reflections. We use a combination of…
On the Local-Global Principle for Integral Apollonian-3 Circle Packings
Xin Zhang
In this paper we study the integral properties of Apollonian-3 circle packings, which are variants of the standard Apollonian circle packings. Specifically, we study the reduction…