Simultaneous Diophantine approximation on manifolds and Hausdorff dimension
نویسندگان
چکیده
منابع مشابه
Diophantine approximation on manifolds and lower bounds for Hausdorff dimension
Given n ∈ N and τ > 1 n , let Sn(τ) denote the classical set of τ approximable points in R, which consists of x ∈ R that lie within distance q from the lattice 1 q Z for infinitely many q ∈ N. In pioneering work, Kleinbock & Margulis showed that for any non-degenerate submanifold M of R and any τ > 1 n almost all points on M are not τ -approximable. Numerous subsequent papers have been geared t...
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In 1998, Kleinbock & Margulis [KM98] established a conjecture of V.G. Sprindzuk in metrical Diophantine approximation (and indeed the stronger Baker-Sprindzuk conjecture). In essence the conjecture stated that the simultaneous homogeneous Diophantine exponent w0(x) = 1/n for almost every point x on a non-degenerate submanifold M of Rn. In this paper the simultaneous inhomogeneous analogue of Sp...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2003
ISSN: 0022-314X
DOI: 10.1016/s0022-314x(02)00035-5