### Abstract

Suppose that m is a positive integer, t = (t_{1},...,t_{m}) ? R^{m}_{+} is a vector of strictly positive numbers, and Q is an infinite set of positive integers. Let W_{Q}(m;t) be the set {x ? R^{m} : ?x_{i}q? < 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 W_{Q}(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 |

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*Bulletin of the London Mathematical Society*, vol. 30, no. 4, pp. 365-376.

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Hausdorff dimension and generalized simultaneous Diophantine approximation

AU - Rynne, Bryan P.

PY - 1998/7

Y1 - 1998/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0032128642&partnerID=8YFLogxK

M3 - Article

VL - 30

SP - 365

EP - 376

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

IS - 4

ER -