Inhomogeneous Diophantine approximation on planar curves
نویسندگان
چکیده
منابع مشابه
Inhomogeneous Diophantine approximation on curves and Hausdorff dimension
The goal of this paper is to develop a coherent theory for inhomogeneous Diophantine approximation on curves in R akin to the well established homogeneous theory. More specifically, the measure theoretic results obtained generalize the fundamental homogeneous theorems of R.C. Baker (1978), Dodson, Dickinson (2000) and Beresnevich, Bernik, Kleinbock, Margulis (2002). In the case of planar curves...
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Let C be a non-degenerate planar curve. We show that the curve is of Khintchine-type for convergence in the case of simultaneous approximation in R 2 with two independent approximation functions; that is if a certain sum converges then the set of all points (x, y) on the curve which satisfy simultaneously the inequalities qx < ψ1(q) and qy < ψ2(q) infinitely often has induced measure 0. This co...
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2010
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-010-0548-9