A problem in non-linear Diophantine approximation
arXiv:1505.06057 · doi:10.1088/1361-6544/aaa498
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.
22 pages, introduction is edited to give concrete applications of our results. An error has been rectified in the proof of the main theorem