# Counting rational points near planar curves

Acta Arithmetica (2014)

- Volume: 165, Issue: 1, page 91-100
- ISSN: 0065-1036

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topAyla Gafni. "Counting rational points near planar curves." Acta Arithmetica 165.1 (2014): 91-100. <http://eudml.org/doc/278925>.

@article{AylaGafni2014,

abstract = {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.},

author = {Ayla Gafni},

journal = {Acta Arithmetica},

keywords = {metric Diophantine approximation; Khinchin-type theorems; planar curves; rational points; approximating functions},

language = {eng},

number = {1},

pages = {91-100},

title = {Counting rational points near planar curves},

url = {http://eudml.org/doc/278925},

volume = {165},

year = {2014},

}

TY - JOUR

AU - Ayla Gafni

TI - Counting rational points near planar curves

JO - Acta Arithmetica

PY - 2014

VL - 165

IS - 1

SP - 91

EP - 100

AB - 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.

LA - eng

KW - metric Diophantine approximation; Khinchin-type theorems; planar curves; rational points; approximating functions

UR - http://eudml.org/doc/278925

ER -

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