Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-24T04:58:36.904Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)