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Bulletin of the London Mathematical Society Advance Access originally published online on February 5, 2009
Bulletin of the London Mathematical Society 2009 41(1):137-146; doi:10.1112/blms/bdn116
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© 2009 London Mathematical Society

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

Natalia Budarina and Detta Dickinson

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

Received 25 April 2008. Revision received 2 September 2008.

It is shown that a non-degenerate curve in Rn satisfies a convergent Groshev theorem with a non-monotonic error function. In other words it is shown that if a volume sum converges the set of points lying on the curve which satisfy a Diophantine condition has Lebesgue measure zero.

2000 Mathematics Subject Classification 11J83.

The first author is supported under the Science Foundation Ireland grant RFP05/MAT00015.


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