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A problem in non-linear Diophantine approximation.

Harrap, S. and Hussain, M. and Kristensen, S. (2018) 'A problem in non-linear Diophantine approximation.', Nonlinearity., 31 (5). pp. 1734-1756.


In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is associated with a class of linear inhomogeneous partial differential equations whose solubility depends on a certain Diophantine condition. The failure of the Diophantine condition guarantees the existence of a smooth solution.

Item Type:Article
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Publisher statement:This is an author-created, un-copyedited version of an article accepted for publication/published in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at
Date accepted:02 January 2018
Date deposited:20 April 2018
Date of first online publication:27 March 2018
Date first made open access:27 March 2019

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