3 citations · 6 across the 4 of their papers we have counts for
6 papers · 1 filter
Asymptotic Density of Apollonian-Type Packings
Matthew Litman, Arseniy Sheydvasser
We consider two seemingly unconnected problems: first, under what circumstances are arithmetic groups like SL(2,O) generated by elementary matrices; second, when do certain classes…
Algebraic Groups Constructed From Rings with Involution
Arseniy Sheydvasser
We define a class of groups constructed from rings equipped with an involution. We show that under suitable conditions, these groups are either algebraic or arithmetic, including a…
The Twisted Euclidean Algorithm: Applications to Number Theory and Geometry
Arseniy, Sheydvasser
We introduce a generalization of the Euclidean algorithm for rings equipped with an involution, and completely enumerate all isomorphism classes of orders over definite, rational q…
Algebraic Groups Constructed from Orders of Quaternion Algebras
Arseniy Sheydvasser
We show that all spin groups of non-definite, quinary quadratic forms over a field with characteristic 0 can be represented as 2 by 2 matrices with entries in an associated quatern…
The Unreasonable Rigidity of Ulam Sets
Joshua Hinman, Borys Kuca, Alexander Schlesinger +1
We give a number of results about families of Ulam sets. Generalizing behavior of Ulam sets U(1,n), we prove using an novel model theoretic approach that there is a rigidity phenom…
A Corrigendum to Unreasonable Slightness
Arseniy Sheydvasser
We revisit Bogdan Nica's 2011 paper, The Unreasonable Slightness of E2 over Imaginary Quadratic Rings, and correct an inaccuracy in his proof.