Diophantine approximation with perfect squares and the solvability of an inhomogeneous wave equation
V. Beresnevich, M. Dodson, S. Kristensen, J. Levesley
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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