Abstract
Suppose that m is a positive integer, t = (t1,...,tm) ? Rm+ is a vector of strictly positive numbers, and Q is an infinite set of positive integers. Let WQ(m;t) be the set {x ? Rm : ?xiq? < q¯ti, 1 = i = m, for infinitely many q ? Q}. In this paper we obtain the Hausdorff dimension of this set. We also consider a generalization of the set WQ(m;t), where the error terms q¯ti in the inequalities are replaced by ?i(q), for general functions ?i satisfying a certain condition at infinity.
Original language | English |
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Pages (from-to) | 365-376 |
Number of pages | 12 |
Journal | Bulletin of the London Mathematical Society |
Volume | 30 |
Issue number | 4 |
Publication status | Published - Jul 1998 |