44 citations · 231 across the 34 of their papers we have counts for
5 papers · 2 filters
The Hausdorff measure version of Gallagher's theorem -- closing the gap and beyond
Mumtaz Hussain, David Simmons
In this paper we prove an upper bound on the "size" of the set of multiplicatively -approximable points in for in terms of -dimensional Hausdorff measure.…
Diophantine approximation in Kleinian groups: singular, extremal, and bad limit points
Victor Beresnevich, Anish Ghosh, David Simmons +1
The overall aim of this note is to initiate a "manifold" theory for metric Diophantine approximation on the limit sets of Kleinian groups. We investigate the notions of singular an…
Badly approximable vectors and fractals defined by conformal dynamical systems
Tushar Das, Lior Fishman, David Simmons +1
We prove that if is the limit set of an irreducible conformal iterated function system (with either finite or countably infinite alphabet), then the badly approximable vectors…
Some manifolds of Khinchin type for convergence
David Simmons
Recently, Beresnevich, Vaughan, Velani, and Zorin (arXiv: 1506.09049) gave some sufficient conditions for a manifold to be of Khinchin type for convergence. We show that their tech…
The Hurwitz continued fraction expansion as applied to real numbers
David Simmons
Hurwitz (1887) defined a continued fraction algorithm for complex numbers which is better behaved in many respects than a more "natural" extension of the classical continued fracti…