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The integer points close to a curve

Published online by Cambridge University Press:  26 February 2010

M. N. Huxley
M. N. Huxley
Affiliation:
School of Mathematics, University of Wales College Cardiff, Senghenydd Road, Cardiff, CF2 4AG.
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§1. Introduction. In this paper, as in [4], we are concerned with integer points (m, n) lying close to the curve

in the sense that

where ║t║ denotes the distance of the real number t from the nearest integer. We shall always suppose that

and that F(x) is at least twice continuously differentiable. Let R be the number of solutions of (1.1) with m an integer, O ≤ m ≤ L. The obvious method of estimating R uses the row-of-teeth or rounding error function

with

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Type
Research Article
Information
Mathematika , Volume 36 , Issue 2 , December 1989 , pp. 198 - 215
Copyright
Copyright © University College London 1989

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References

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