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

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

2005-12-29

arxiv.org/abs/math/0512644v1

Mathematics

Analysis of PDEs

20 pages

Scientific paper

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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