An Approximation by Lacunary Sequence of Vectors
نویسنده
چکیده
Let (tk)k=0 be a sequence of real numbers satisfying t0 6= 0 and |tk+1| > (1+ 1/M)|tk| for each k > 0, where M > 1 is a fixed number. We prove that for any sequence of real numbers (ξk)k=0 there is a real number ξ such that ||tkξ−ξk|| > 1/(80M log(28M)) for each k > 0. Here, ||x|| denotes the distance from x ∈ R to the nearest integer. This is a corollary derived from our main theorem which is a more general matrix version of this statement with explicit constants.
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عنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 17 شماره
صفحات -
تاریخ انتشار 2008