4 citations · 4 across the 3 of their papers we have counts for
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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…
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…