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An inhomogeneous wave equation and non-linear Diophantine approximation

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JournalAdvances in Mathematics
DatePublished - 30 Jan 2008
Issue number2
Volume217
Number of pages21
Pages (from-to)740-760
Original languageEnglish

Abstract

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. (c) 2007 Elsevier Inc. All rights reserved.

    Research areas

  • Diophantine approximation, Hausdorff dimension, wave equation, small denominators problem, Diophantine phenomena, HAUSDORFF DIMENSION, SOLVABILITY, VECTORS, FORMS, SETS

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