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arXiv · 1505.06057

A problem in non-linear Diophantine approximation

Stephen Harrap·Mumtaz Hussain·Simon Kristensen
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Abstract

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.

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Stephen Harrap, Mumtaz Hussain, Simon Kristensen. 2015-05-22. A problem in non-linear Diophantine approximation. https://doi.org/10.1088/1361-6544%2Faaa498

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