Diophantine approximation with perfect squares and the solvability of an inhomogeneous wave equation

V. Beresnevich; M. Dodson; S. Kristensen; J. Levesley

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Diophantine approximation with perfect squares and the solvability of an inhomogeneous wave equation

V. Beresnevich·M. Dodson·S. Kristensen·J. Levesley

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Abstract

The Hausdorff dimension of an exceptional set of periods for which convergence of a formal solution to an inhomogeneous wave equation in n spatial and one temporal dimension is problematic, is determined along with conditions which the periods must satisfy to ensure the solvability of the inhomogeneous wave equation by a smooth periodic function. To derive this information, a complete metric theory for a related fully nonlinear Diophantine approximation problem involving perfect squares is established.

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V. Beresnevich, M. Dodson, S. Kristensen, J. Levesley. 2005-12-29. Diophantine approximation with perfect squares and the solvability of an inhomogeneous wave equation. https://arxiv.org/abs/math/0512644

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