Hausdorff dimension and generalized simultaneous Diophantine approximation

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)365-376
Number of pages12
JournalBulletin of the London Mathematical Society
Volume30
Issue number4
Publication statusPublished - Jul 1998

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Diophantine Approximation
Simultaneous Approximation
Hausdorff Dimension
Integer
Strictly positive
Error term
Infinity

Cite this

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Hausdorff dimension and generalized simultaneous Diophantine approximation. / Rynne, Bryan P.

In: Bulletin of the London Mathematical Society, Vol. 30, No. 4, 07.1998, p. 365-376.

Research output: Contribution to journalArticle

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