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Fractional part sums and lattice points

Published online by Cambridge University Press:  20 January 2009

Werner Georg Nowak
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Abstract

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The objective of this article are sums S(M)=∑n;ψ(Mf(n/M)) where ψdenotes essentially the fractional part minus ½, f is a C4-function with fn nonvanishing, and summation is extended over an interval of order M. For S(M) an Ω-estimate and a mean-square bound is obtained. Applications to problems concerning the number of lattice points in large planar domains are discussed.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 41 , Issue 3 , October 1998 , pp. 497 - 515
Copyright
Copyright © Edinburgh Mathematical Society 1998

Footnotes

*

This article is part of a research project supported by the Austrian Science Foundation (Nr. P 9892-PHY).

References

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