Abstract
Let \(S\) be a bounded closed convex plane set with sufficiently smooth boundary curve. The area of \(S\) is the number of integer points in \(S\) minus a correction, the local discrepancy. Kendall’s classic paper introduced the Fourier transform of the local discrepancy and found the best possible mean square estimate. We obtain a corresponding fourth power estimate, valid merely under a \(C^2\) smoothness condition.
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