### Abstract

Let m, n, be positive integers and let Q be an infinite subset of Z^{n}. For any number t, define the set [formula]. It is shown in this paper that if ? ? [0, n] is the unique number such that the series [formula] is convergent when e{lunate} > 0 but divergent when e{lunate} < 0, then the Hausdorff dimension of the set E_{Q}(m, n; t) is dim E_{Q}(m, n; t) = mn - 1 + (1 + ?)/(1 + t), for all t > ?. © 1994 Academic Press. All rights reserved.

Original language | English |
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Pages (from-to) | 75-79 |

Number of pages | 5 |

Journal | Journal of Number Theory |

Volume | 48 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul 1994 |

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**The Hausdorff Dimension of Sets of Points Whose Simultaneous Rational Approximation by Sequences of Integer Vectors Have Errors with Small Product.** / Rynne, B. P.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The Hausdorff Dimension of Sets of Points Whose Simultaneous Rational Approximation by Sequences of Integer Vectors Have Errors with Small Product

AU - Rynne, B. P.

PY - 1994/7

Y1 - 1994/7

N2 - Let m, n, be positive integers and let Q be an infinite subset of Zn. For any number t, define the set [formula]. It is shown in this paper that if ? ? [0, n] is the unique number such that the series [formula] is convergent when e{lunate} > 0 but divergent when e{lunate} < 0, then the Hausdorff dimension of the set EQ(m, n; t) is dim EQ(m, n; t) = mn - 1 + (1 + ?)/(1 + t), for all t > ?. © 1994 Academic Press. All rights reserved.

AB - Let m, n, be positive integers and let Q be an infinite subset of Zn. For any number t, define the set [formula]. It is shown in this paper that if ? ? [0, n] is the unique number such that the series [formula] is convergent when e{lunate} > 0 but divergent when e{lunate} < 0, then the Hausdorff dimension of the set EQ(m, n; t) is dim EQ(m, n; t) = mn - 1 + (1 + ?)/(1 + t), for all t > ?. © 1994 Academic Press. All rights reserved.

UR - http://www.scopus.com/inward/record.url?scp=43949161623&partnerID=8YFLogxK

U2 - 10.1006/jnth.1994.1053

DO - 10.1006/jnth.1994.1053

M3 - Article

VL - 48

SP - 75

EP - 79

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 1

ER -