A note on rational points near planar curves
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.
| Main Author: | |
|---|---|
| Format: | Journal article |
| Published: |
Polskiej Akademii Nauk, Instytut Matematyczny
2017
|
| _version_ | 1826277229275906048 |
|---|---|
| author | Chow, S |
| author_facet | Chow, S |
| author_sort | Chow, S |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T23:25:46Z |
| format | Journal article |
| id | oxford-uuid:6a4fef1b-253d-42de-b4d5-5b5c56e7ff61 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:25:46Z |
| publishDate | 2017 |
| publisher | Polskiej Akademii Nauk, Instytut Matematyczny |
| record_format | dspace |
| spelling | oxford-uuid:6a4fef1b-253d-42de-b4d5-5b5c56e7ff612022-03-26T18:56:37ZA note on rational points near planar curvesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:6a4fef1b-253d-42de-b4d5-5b5c56e7ff61Symplectic Elements at OxfordPolskiej Akademii Nauk, Instytut Matematyczny2017Chow, SUnder 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. |
| spellingShingle | Chow, S A note on rational points near planar curves |
| title | A note on rational points near planar curves |
| title_full | A note on rational points near planar curves |
| title_fullStr | A note on rational points near planar curves |
| title_full_unstemmed | A note on rational points near planar curves |
| title_short | A note on rational points near planar curves |
| title_sort | note on rational points near planar curves |
| work_keys_str_mv | AT chows anoteonrationalpointsnearplanarcurves AT chows noteonrationalpointsnearplanarcurves |