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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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.

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
URI:	https://orca.cardiff.ac.uk/id/eprint/58595

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