| Texto completo | |
| Autor(es): |
Alves, Carina
;
Strapasson, Joao E.
;
De Araujo, Robson R.
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | ARCHIV DER MATHEMATIK; v. N/A, p. 10-pg., 2024-10-29. |
| Resumo | |
In this paper, we study properties of well-rounded ideal lattices focusing on the lower bounds for their minimum norm. We present counterexamples showing that the stated bounds in a previous work do not hold for mixed number fields through the canonical embedding. However, we prove that ideal lattices obtained via the Minkowski embedding (instead of the canonical embedding) are well-rounded if and only if the number field is cyclotomic. Additionally, we derive new lower bounds for the minimum norm of ideal lattices under both the canonical and twisted embeddings. Our results not only refine existing theories but also open new possibilities for research on well-rounded ideal lattices in higher dimensions. (AU) | |
| Processo FAPESP: | 20/09838-0 - BI0S - Brazilian Institute of Data Science |
| Beneficiário: | João Marcos Travassos Romano |
| Modalidade de apoio: | Auxílio à Pesquisa - Programa Centros de Pesquisa Aplicada |
| Processo FAPESP: | 23/15735-8 - Reticulados bem arredondados no R² via o homomorfismo canônico e o homomorfismo torcido |
| Beneficiário: | Nicoll Vanessa Jerez Nieves |
| Modalidade de apoio: | Bolsas no Brasil - Iniciação Científica |
| Processo FAPESP: | 22/12667-9 - Números algébricos, reticulados e aplicações |
| Beneficiário: | Cleber Luiz de Oliveira Santos |
| Modalidade de apoio: | Bolsas no Brasil - Iniciação Científica |