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A fourth power discrepancy mean

Huxley, Martin Neil 2014. A fourth power discrepancy mean. Monatshefte für Mathematik 173 (2) , pp. 231-238. 10.1007/s00605-013-0558-2

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Springer
ISSN: 0026-9255
Last Modified: 05 Mar 2019 14:24

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