Simultaneous diophantine approximation for a restricted class of pairs of real numbers
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910914424340480 |
|---|---|
| author | Lazar, Youssef |
| author_facet | Lazar, Youssef |
| contents | We prove that the Littlewood conjecture is satisfied for a restricted class of pairs $(α,β)$ of badly approximable numbers. We use the localization of the roots of a cubic equation with coefficients depending on the diophantine properties for the considered pair $(α,β)$. The estimates of the roots rely on the properties of the denominators of the convergents of the continued fraction expansion of $α$ and $β$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_01596 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Simultaneous diophantine approximation for a restricted class of pairs of real numbers Lazar, Youssef Number Theory We prove that the Littlewood conjecture is satisfied for a restricted class of pairs $(α,β)$ of badly approximable numbers. We use the localization of the roots of a cubic equation with coefficients depending on the diophantine properties for the considered pair $(α,β)$. The estimates of the roots rely on the properties of the denominators of the convergents of the continued fraction expansion of $α$ and $β$. |
| title | Simultaneous diophantine approximation for a restricted class of pairs of real numbers |
| topic | Number Theory |
| url | https://arxiv.org/abs/2202.01596 |