A note on rational points near planar curves

Samuel Khai Ho Chow

doi:10.4064/aa8622-11-2016

A note on rational points near planar curves

Samuel Khai Ho Chow

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Under fairly natural assumptions, Huang counted the number of rational points lying close to an arc of a planar curve. He obtained upper and lower bounds of the correct order of magnitude, and conjectured an asymptotic formula. In this note, we establish the conjectured asymptotic formula.

Original language	English
Pages (from-to)	393-396
Number of pages	4
Journal	Acta Arithmetica
Volume	177
DOIs	https://doi.org/10.4064/aa8622-11-2016
Publication status	Published - 22 Feb 2017

Bibliographical note

This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

Keywords

Metric diophantine approximation
Rational points near curves

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10.4064/aa8622-11-2016

TemplateVersion_ANoteOnRationalPointsNearPlanarCurves
This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.
Accepted author manuscript, 222 KB

Programme Grant-New Frameworks in metric Number Theory
Velani, S. & Beresnevich, V.
EPSRC
1/06/12 → 30/11/18
Project: Research project (funded) › Research

Cite this

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AB - Under fairly natural assumptions, Huang counted the number of rational points lying close to an arc of a planar curve. He obtained upper and lower bounds of the correct order of magnitude, and conjectured an asymptotic formula. In this note, we establish the conjectured asymptotic formula.

KW - Metric diophantine approximation

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DO - 10.4064/aa8622-11-2016

M3 - Article

SN - 0065-1036

VL - 177

SP - 393

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JO - Acta Arithmetica

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ER -

A note on rational points near planar curves

Abstract

Bibliographical note

Keywords

Access to Document

Projects

Programme Grant-New Frameworks in metric Number Theory

Cite this