A problem in non-linear Diophantine approximation

Harrap, S.; Hussain, M.; Kristensen, S.

doi:10.1088/1361-6544/aaa498

A problem in non-linear Diophantine approximation

Harrap, S.; Hussain, M.; Kristensen, S.

Authors

Dr Stephen Harrap s.g.harrap@durham.ac.uk
Assistant Professor

M. Hussain

S. Kristensen

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.

Citation

Harrap, S., Hussain, M., & Kristensen, S. (2018). A problem in non-linear Diophantine approximation. Nonlinearity, 31(5), 1734-1756. https://doi.org/10.1088/1361-6544/aaa498

Journal Article Type	Article
Acceptance Date	Jan 2, 2018
Online Publication Date	Mar 27, 2018
Publication Date	May 1, 2018
Deposit Date	Dec 30, 2015
Publicly Available Date	Mar 27, 2019
Journal	Nonlinearity
Print ISSN	0951-7715
Electronic ISSN	1361-6544
Publisher	IOP Publishing
Peer Reviewed	Peer Reviewed
Volume	31
Issue	5
Pages	1734-1756
DOI	https://doi.org/10.1088/1361-6544/aaa498
Related Public URLs	http://arxiv.org/abs/1505.06057

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Copyright 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 https://doi.org/10.1088/1361-6544/aaa498