An inhomogeneous wave equation and non-linear Diophantine approximation

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Published copy (DOI)

10.1016/j.aim.2007.09.003

Author(s)

Victor Beresnevich
M. M. Dodson
Simon Kristensen
Jason Levesley

Department/unit(s)

Mathematics

Publication details

Journal	Advances in Mathematics
Date	Published - 30 Jan 2008
Issue number	2
Volume	217
Number of pages	21
Pages (from-to)	740-760
Original language	English

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