Siegel's lemma with additional conditions
| dc.creator | Fukshansky, Lenny | |
| dc.date | 2004-09-21 | |
| dc.date | 2005-11-03 | |
| dc.date.accessioned | 2026-07-07T08:12:19Z | |
| dc.date.available | 2026-07-07T08:12:19Z | |
| dc.description | Let $K$ be a number field, and let $W$ be a subspace of $K^N$, $N \geq 1$. Let $V_1,...,V_M$ be subspaces of $K^N$ of dimension less than dimension of $W$. We prove the existence of a point of small height in $W \setminus \bigcup_{i=1}^M V_i$, providing an explicit upper bound on the height of such a point in terms of heights of $W$ and $V_1,...,V_M$. Our main tool is a counting estimate we prove for the number of points of a subspace of $K^N$ inside of an adelic cube. As corollaries to our main result we derive an explicit bound on the height of a non-vanishing point for a decomposable form and an effective subspace extension lemma. | |
| dc.description | 12 pages, revised version, to appear in Journal of Number Theory | |
| dc.identifier | https://arxiv.org/abs/math/0409375 | |
| dc.identifier | http://arxiv.org/abs/math/0409375 | |
| dc.identifier | J. Number Theory 120 (2006), no. 1, 13--25 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132411 | |
| dc.subject | Number Theory | |
| dc.subject | 11D04; 11H06; 11H46 | |
| dc.title | Siegel's lemma with additional conditions | |
| dc.type | text |