83 citations · 293 across the 29 of their papers we have counts for
5 papers · 2 filters
Intrinsic Diophantine approximation on manifolds: General theory
Lior Fishman, Dmitry Kleinbock, Keith Merrill +1
We investigate the question of how well points on a nondegenerate -dimensional submanifold can be approximated by rationals also lying on , establis…
Decaying and non-decaying badly approximable numbers
Ryan Broderick, Lior Fishman, David Simmons
We call a badly approximable number if, roughly, the Lagrange constants of integer multiples of that number decay as fast as possible. In this terminology, a question of…
Variations on Dirichlet's theorem
Lior Fishman, David Simmons
We give a necessary and sufficient condition for the following property of an integer and a pair : There exist and suc…
The Banach-Mazur-Schmidt game and the Banach-Mazur-McMullen game
Lior Fishman, Vanessa Reams, David Simmons
We introduce two new mathematical games, the Banach-Mazur-Schmidt game and the Banach-Mazur-McMullen game, merging well-known games. We investigate the properties of the games, as…
Hausdorff dimensions of very well intrinsically approximable subsets of quadratic hypersurfaces
Lior Fishman, Keith Merrill, David Simmons
We prove an analogue of a theorem of A. Pollington and S. Velani ('05), furnishing an upper bound on the Hausdorff dimension of certain subsets of the set of very well intrinsicall…