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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