منابع مشابه
Simultaneous Diophantine Approximation
Using a method suggested by E. S. Barnes, it is shown that the simultaneous inequalities r(p — arf < c, r(q — fir) < c have an infinity of integral solutions p, q, r (with r > 0), for arbitrary irrationals a and /3, provided that c > 1/2.6394. This improves an earlier result of Davenport, who shows that the same conclusion holds if c > 1/46"" = 1/2.6043 • • •.
متن کاملSimultaneous Diophantine Approximation on Planar
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...
متن کاملDistributed computing of simultaneous Diophantine approximation problems
In this paper we present the Multithreaded Advanced Fast Rational Approximation algorithm – MAFRA – for solving n-dimensional simultaneous Diophantine approximation problems. We show that in some particular applications the Lenstra-Lenstra-Lovász (L) algorithm can be substituted by the presented one in order to reduce their practical running time. MAFRA was implemented in the following architec...
متن کاملSimultaneous inhomogeneous Diophantine approximation on manifolds
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...
متن کاملA Note on Simultaneous Diophantine Approximation in Positive Characteristic
In a recent paper, Inoue and Nakada proved a 0-1 law and a strong law of large numbers with error term for the number of coprime solutions of the one-dimensional Diophantine approximation problem in the field of formal Laurent series over a finite base field. In this note, we generalize their results to higher dimensions.
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1977
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700020292