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A problem in non-linear Diophantine approximation

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  • Stephen Harrap, Durham University
  • ,
  • Mumtaz Hussain, La Trobe University
  • ,
  • Simon Kristensen

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.

OriginalsprogEngelsk
TidsskriftNonlinearity
Vol/bind31
Nummer5
Sider (fra-til)1734-1756
Antal sider23
ISSN0951-7715
DOI
StatusUdgivet - 27 mar. 2018

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