A problem in non-linear Diophantine approximation. (27th March 2018) - Harrap, Stephen; Hussain, Mumtaz; Kristensen, Simon
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.