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Diophantine approximation on non-degenerate curves with non-monotonic error function

Authors:	Budarina Natalia; Dickinson Detta

Institution:	Department of Mathematics Logic House National University of Ireland, Maynooth Co Kildare Republic of Ireland nbudarina@maths.nuim.ie

Abstract:	It is shown that a non-degenerate curve in $R$ ⁿ satisfies a convergentGroshev theorem with a non-monotonic error function. In otherwords it is shown that if a volume sum converges the set ofpoints lying on the curve which satisfy a Diophantine conditionhas Lebesgue measure zero.

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