A problem in non-linear Diophantine approximation
Number Theory
2018-04-25 v2
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.
Cite
@article{arxiv.1505.06057,
title = {A problem in non-linear Diophantine approximation},
author = {Stephen Harrap and Mumtaz Hussain and Simon Kristensen},
journal= {arXiv preprint arXiv:1505.06057},
year = {2018}
}
Comments
22 pages, introduction is edited to give concrete applications of our results. An error has been rectified in the proof of the main theorem