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THE METRIC THEORY OF MIXED TYPE LINEAR FORMS

DETTA DICKINSON

Department of Mathematics & Statistics, NUI Maynooth, Co. Kildare, Republic of Ireland

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and

MUMTAZ HUSSAIN

Department of Mathematics and Statistics, Latrobe University, Melbourne, 3086 VIC, Australia

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https://doi.org/10.1142/S1793042112501278Cited by:6 (Source: Crossref)

Abstract

In this paper the metric theory of Diophantine approximation of linear forms that are of mixed type is investigated. Khintchine–Groshev theorems are established together with the Hausdorff measure generalizations. The latter includes the original dimension results obtained in [H. Dickinson, The Hausdorff dimension of sets arising in metric Diophantine approximation, Acta Arith.68(2) (1994) 133–140] as special cases.

Keywords:

AMSC: 11J83, 11J13, 11K60

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