The Hausdorff dimension of systems of simultaneously small linear forms

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Simultaneous Diophantine Approximation on Polynomial Curves

The Hausdorff dimension and measure of the set of simultaneously ψ-approximable points lying on integer polynomial curves is obtained for sufficiently small error functions

Hausdorff dimension and p-adic diophantine approximation

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Simultaneous Diophantine approximation of integral polynomials in the different metrics

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Ideas and results from the theory of Diophantine approximation

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The metric theory of mixed type linear forms

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 case

On the Number of Polynomials with Small Discriminants in the Euclidean and p-adic Metrics

In this article it is proved that there exist a large number of polynomials which have small discriminant in terms of the Euclidean and p-adic metrics simultaneously. The measure of the set of points which satisfy certain polynomial a nd derivative conditions is also determine