The density of rational points in curves and surfaces
| dc.creator | Heath-Brown, D. R. | |
| dc.creator | Colliot-Thélène, J. -L. | |
| dc.date | 2004-05-20 | |
| dc.date.accessioned | 2026-07-07T05:08:25Z | |
| dc.date.available | 2026-07-07T05:08:25Z | |
| dc.description | Let $X$ be an algebraic variety, defined over the rationals. This paper gives upper bounds for the number of rational points on $X$, with height at most $B$, for the case in which $X$ is a curve or a surface. In the latter case one excludes from the counting function those points that lie on lines in the surface. The bounds are uniform for all $X$ of a given degree. They are best possible in the case of curves. As an application it is shown that if $F$ is an irreducible binary form of degree 3 or more then almost all integers represented by $F$ have essentially one such representation. | |
| dc.description | 46 pages, published version; appendix by J.-L. Colliot-Thélène | |
| dc.identifier | https://arxiv.org/abs/math/0405392 | |
| dc.identifier | http://arxiv.org/abs/math/0405392 | |
| dc.identifier | Ann. of Math. (2), Vol. 155 (2002), no. 2, 553--598 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71256 | |
| dc.subject | Number Theory | |
| dc.title | The density of rational points in curves and surfaces | |
| dc.type | text |