Lattice Points in Large Borel Sets and Successive Minima
| dc.creator | Aliev, Iskander | |
| dc.creator | Gruber, Peter | |
| dc.date | 2005-10-08 | |
| dc.date.accessioned | 2026-07-07T06:47:14Z | |
| dc.date.available | 2026-07-07T06:47:14Z | |
| dc.description | Let $B$ be a Borel set in $\mathbb E^{d}$ with volume $V(B)=\infty$. It is shown that almost all lattices $L$ in $\mathbb E^{d}$ contain infinitely many pairwise disjoint $d$-tuples, that is sets of $d$ linearly independent points in $B$. A consequence of this result is the following: let $S$ be a star body in $\mathbb E^{d}$ with $V(S)=\infty$. Then for almost all lattices $L$ in $\mathbb E^{d}$ the successive minima $λ_{1}(S,L),..., λ_{d}(S,L)$ of $S$ with respect to $L$ are 0. A corresponding result holds for most lattices in the Baire category sense. A tool for the latter result is the semi-continuity of the successive minima. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0510163 | |
| dc.identifier | http://arxiv.org/abs/math/0510163 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103590 | |
| dc.subject | Number Theory | |
| dc.subject | 11H16; 11H50; 11J25 | |
| dc.title | Lattice Points in Large Borel Sets and Successive Minima | |
| dc.type | text |