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A note on rational points near planar curves

Volume 177 / 2017

Sam Chow Acta Arithmetica 177 (2017), 393-396 MSC: Primary 11J83; Secondary 11J13. DOI: 10.4064/aa8622-11-2016 Published online: 22 February 2017

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.

Authors

  • Sam ChowDepartment of Mathematics
    University of York
    Heslington, York, YO10 5DD
    United Kingdom
    e-mail

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