A problem in non-linear Diophantine approximation

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

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
• Public URL: https://durham-repository.worktribe.com/output/1393248
• Related Public URLs: http://arxiv.org/abs/1505.06057