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An inhomogeneous wave equation and non-linear Diophantine approximation

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  • V. Beresnevich, University of York, United Kingdom
  • M. M. Dodson, University of York, United Kingdom
  • S. Kristensen
  • J. Levesley, University of York, United Kingdom
  • Department of Mathematical Sciences
A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution is studied. Both the Lebesgue and Hausdorff measures of this set are obtained.
Original languageEnglish
JournalAdvances in Mathematics
Pages (from-to)740-760
Number of pages21
Publication statusPublished - 2008

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