Geodesic
Counting rational points near planar curves
Ayla Gafni1
1 Department of Mathematics Pennsylvania State University 109 McAllister Bldg University Park, PA 16802, U.S.A.
Acta Arithmetica, Tome 165 (2014) no. 1, pp. 91-100

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $[\eta ,\xi ]$, then the number of rational points with denominator no larger than $Q$ that lie within a $\delta $-neighborhood of the graph of $f$ is shown to be asymptotically equivalent to $(\xi -\eta )\delta Q^2$.
DOI : 10.4064/aa165-1-5
Keywords: asymptotic formula number rational points near planar curves precisely mathbb rightarrow mathbb sufficiently smooth function defined interval eta number rational points denominator larger lie within delta neighborhood graph shown asymptotically equivalent eta delta

Ayla Gafni 1

1 Department of Mathematics Pennsylvania State University 109 McAllister Bldg University Park, PA 16802, U.S.A. 
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Ayla Gafni. Counting rational points near planar curves. Acta Arithmetica, Tome 165 (2014) no. 1, pp. 91-100. doi: 10.4064/aa165-1-5

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