4 citations · 4 across the 3 of their papers we have counts for
8 papers
Diophantine approximation on abelian varieties; a conjecture of M. Waldschmidt
Lior Fishman, David Lambert, Keith Merrill +1
Following the work of Waldschmidt, we investigate problems in Diophantine approximation on abelian varieties. First we show that a conjecture of Waldschmidt for a given simple abel…
Imputation under Differential Privacy
Soumojit Das, Jorg Drechsler, Keith Merrill +1
The literature on differential privacy almost invariably assumes that the data to be analyzed are fully observed. In most practical applications this is an unrealistic assumption.…
Uniformly de Bruijn sequences and symbolic Diophantine approximation on fractals
Lior Fishman, Keith Merrill, David Simmons
Intrinsic Diophantine approximation on fractals, such as the Cantor ternary set, was undoubtedly motivated by questions asked by K. Mahler (1984). One of the main goals of this pap…
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…
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…
Intrinsic Diophantine approximation on quadric hypersurfaces
Lior Fishman, Dmitry Kleinbock, Keith Merrill +1
We consider the question of how well points in a quadric hypersurface can be approximated by rational points of . This contrasts with the m…
Rational Approximation on Spheres
Dmitry Kleinbock, Keith Merrill
We quantify the density of rational points in the unit sphere , proving analogues of the classical theorems on the embedding of $\q^n$ into $\r^n$. Specifically, we prove a Di…
Limit Points Badly Approximable by Horoballs
Dustin Mayeda, Keith Merrill
For a proper, geodesic, Gromov hyperbolic metric space X, a discrete subgroup of isometries Γwhose limit set is uniformly perfect, and a disjoint collection of horoballs {H_j}, we…