On binary quadratic forms with semigroup property
| dc.creator | Aicardi, Francesca | |
| dc.creator | Timorin, Vladlen | |
| dc.date | 2004-12-07 | |
| dc.date | 2005-11-18 | |
| dc.date.accessioned | 2026-07-07T06:39:08Z | |
| dc.date.available | 2026-07-07T06:39:08Z | |
| dc.description | A quadratic form f is said to have semigroup property if its values at points of the integer lattice form a semigroup under multiplication. A problem of V. Arnold is to describe all binary integer quadratic forms with semigroup property. If there is an integer bilinear map s such that f(s(x,y))=f(x)f(y) for all vectors x and y from the integer 2-dimensional lattice, then the form f has semigroup property. We give an explicit description of all pairs (f,s) with the property stated above. We do not know any other examples of forms with semigroup property. | |
| dc.description | v3: minor changes, referenced added; 28 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0412145 | |
| dc.identifier | http://arxiv.org/abs/math/0412145 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100971 | |
| dc.subject | Number Theory | |
| dc.subject | 11E16; 11E41 | |
| dc.title | On binary quadratic forms with semigroup property | |
| dc.type | text |