We find an asymptotic formula for the number of rational points near planar curves. More precisely, if f:ℝ → 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)δQ².
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa165-1-5,
author = {Ayla Gafni},
title = {Counting rational points near planar curves},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {91-100},
zbl = {1316.11065},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa165-1-5}
}
Ayla Gafni. Counting rational points near planar curves. Acta Arithmetica, Tome 166 (2014) pp. 91-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa165-1-5/