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The integer points close to a curve
Published online by Cambridge University Press: 26 February 2010
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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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