Counting rational points near planar curves

Ayla Gafni

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arXiv · 1401.4958

Counting rational points near planar curves

Ayla Gafni

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Abstract

We find an asymptotic formula for the number of rational points near planar curves. More precisely, if $f:\mathbb{R}\rightarrow\mathbb{R}$ is a sufficiently smooth function defined on the interval $[η,ξ]$, then the number of rational points with denominator no larger than $Q$ that lie within a $δ$-neighborhood of the graph of $f$ is shown to be asymptotically equivalent to $(ξ-η)δQ^2$.

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BibTeX RIS

Ayla Gafni. 2014-01-20. Counting rational points near planar curves. https://arxiv.org/abs/1401.4958

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