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HAUSDORFF DIMENSION AND GENERALIZED SIMULTANEOUS DIOPHANTINE APPROXIMATION

Published online by Cambridge University Press:  01 July 1998

BRYAN P. RYNNE
BRYAN P. RYNNE
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS
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Abstract

Suppose that m is a positive integer, τ=(τ1, …, τm) ∈ℝm+ is a vector of strictly positive numbers, and Q is an infinite set of positive integers. Let WQ(m; τ) be the set

formula here

In this paper we obtain the Hausdorff dimension of this set. We also consider a generalization of the set WQ(m; τ), where the error terms q−τi in the inequalities are replaced by ψi(q), for general functions ψi satisfying a certain condition at infinity.

Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 4 , July 1998 , pp. 365 - 376
Copyright
© The London Mathematical Society 1998

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