Klein polyhedra and lattices with positive norm minima
| dc.creator | German, Oleg N. | |
| dc.date | 2005-04-23 | |
| dc.date | 2006-06-04 | |
| dc.date.accessioned | 2026-07-07T06:39:50Z | |
| dc.date.available | 2026-07-07T06:39:50Z | |
| dc.description | A Klein polyhedron is defined as the convex hull of nonzero lattice points inside an orthant of $\R^n$. It generalizes the concept of continued fraction. In this paper facets and edge stars of vertices of a Klein polyhedron are considered as multidimensional analogs of partial quotients and quantitative characteristics of these ``partial quotients'', so called determinants, are defined. It is proved that the facets of all the $2^n$ Klein polyhedra generated by a lattice $\La$ have uniformly bounded determinants if and only if the facets and the edge stars of the vertices of the Klein polyhedron generated by $\La$ and related to the positive orthant have uniformly bounded determinants. | |
| dc.description | 12 pages, 18 references | |
| dc.identifier | https://arxiv.org/abs/math/0504483 | |
| dc.identifier | http://arxiv.org/abs/math/0504483 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101226 | |
| dc.subject | Number Theory | |
| dc.subject | 11H06, 11H46, 11H50 (Primary), 52C07 (Secondary) | |
| dc.title | Klein polyhedra and lattices with positive norm minima | |
| dc.type | text |