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The mean lattice point discrepancy

Published online by Cambridge University Press:  20 January 2009

M. N. Huxley
M. N. Huxley
Affiliation:
School of Mathematics, University of Wales College of Cardiff, 23, Senghenydd Road, Cardiff CF2 4YH
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Abstract

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Consider a sufficiently smooth simple closed convex plane curve enclosing the origin, expanding linearly with time. The root mean square of the discrepancy (number of lattice points minus area) from time t = M to t = M + 1 is almost as small as the root mean square discrepancy from time t = 0 to t = M, so the discrepancy has no memory.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 3 , October 1995 , pp. 523 - 531
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

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