The density of rational points on non-singular hypersurfaces, I
| dc.creator | Browning, T. D. | |
| dc.creator | Heath-Brown, D. R. | |
| dc.date | 2005-02-11 | |
| dc.date | 2006-01-03 | |
| dc.date.accessioned | 2026-07-07T06:39:25Z | |
| dc.date.available | 2026-07-07T06:39:25Z | |
| dc.description | Let $X \subset \mathbb{P}^n$ be a non-singular hypersurface of degree $d>1$, and let $ε>0$. This paper is concerned with the conjecture that there are $O(B^{n-1+ε})$ rational points on $X$ that have height at most $B$, in which the implied constant is allowed to depend only upon $d, ε$ and $n$. In particular this conjecture is shown to hold as soon as $d>4$. Furthermore, the main ideas in the proof are used to obtain new paucity estimates for certain diophantine equations. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0502243 | |
| dc.identifier | http://arxiv.org/abs/math/0502243 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101073 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G35 (11P05,14G05) | |
| dc.title | The density of rational points on non-singular hypersurfaces, I | |
| dc.type | text |