Integral points of small height outside of a hypersurface
| dc.creator | Fukshansky, Lenny | |
| dc.date | 2004-09-21 | |
| dc.date | 2005-11-03 | |
| dc.date.accessioned | 2026-07-07T08:12:18Z | |
| dc.date.available | 2026-07-07T08:12:18Z | |
| dc.description | Let $F$ be a non-zero polynomial with integer coefficients in $N$ variables of degree $M$. We prove the existence of an integral point of small height at which $F$ does not vanish. Our basic bound depends on $N$ and $M$ only. We separately investigate the case when $F$ is decomposable into a product of linear forms, and provide a more sophisticated bound. We also relate this problem to a certain extension of Siegel's Lemma as well as to Faltings' version of it. Finally we exhibit an application of our results to a discrete version of the Tarski plank problem. | |
| dc.description | 16 pages, revised version, to appear in Monatshefte für Mathematik | |
| dc.identifier | https://arxiv.org/abs/math/0409374 | |
| dc.identifier | http://arxiv.org/abs/math/0409374 | |
| dc.identifier | Monatsh. Math. 147 (2006), no. 1, 25--41 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132410 | |
| dc.subject | Number Theory | |
| dc.subject | 11C08; 11H06; 11D04; 11H46 | |
| dc.title | Integral points of small height outside of a hypersurface | |
| dc.type | text |