ZERO‐ONE LAWS IN SIMULTANEOUS AND MULTIPLICATIVE DIOPHANTINE APPROXIMATION
نویسندگان
چکیده
منابع مشابه
Multiplicative Diophantine approximation
In his paper, Dirichlet gives a complete proof for n = 1 and observes that this proof can be easily extended to arbitrary values of n. Good references on this topic are Chapter II of [52] and Cassels’ book [17]. There are in the literature many papers on various generalisations of the Dirichlet Theorem and on closely related problems. A typical question asks whether for a given set of mn real n...
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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: Mathematika
سال: 2013
ISSN: 0025-5793,2041-7942
DOI: 10.1112/s0025579312001106