On a mixed problem in Diophantine approximation
| hal.structure.identifier | Institut de Recherche Mathématique Avancée [IRMA] | |
| hal.structure.identifier | Département de Mathématiques (Evry) | |
| dc.contributor.author | BUGEAUD, Yann | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DE MATHAN, Bernard | |
| dc.date.accessioned | 2024-04-04T02:41:19Z | |
| dc.date.available | 2024-04-04T02:41:19Z | |
| dc.date.created | 2009-03-11 | |
| dc.date.issued | 2009 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191142 | |
| dc.description.abstractEn | Let $d$ be a positive integer. Let $p$ be a prime number. Let $\alpha$ be a real algebraic number of degree $d+1$. We establish that there exist a positive constant $c$ and infinitely many algebraic numbers $\xi$ of degree $d$ such that $|\alpha - \xi| \cdot \min\{|\Norm(\xi)|_p,1\} < c H(\xi)^{-d-1} \, (\log 3 H(\xi))^{-1/d}$. Here, $H(\xi)$ and $\Norm(\xi)$ denote the na\"\i ve height of $\xi$ and its norm, respectively. This extends an earlier result of de Mathan and Teulié that deals with the case $d=1$. | |
| dc.language.iso | en | |
| dc.publisher | Instytut Matematyczny PAN | |
| dc.title.en | On a mixed problem in Diophantine approximation | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 0903.2741 | |
| bordeaux.journal | Acta Arithmetica | |
| bordeaux.page | à paraître | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00367593 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00367593v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Acta%20Arithmetica&rft.date=2009&rft.spage=%C3%A0%20para%C3%AEtre&rft.epage=%C3%A0%20para%C3%AEtre&rft.au=BUGEAUD,%20Yann&DE%20MATHAN,%20Bernard&rft.genre=article |
Files in this item
| Files | Size | Format | View |
|---|---|---|---|
|
There are no files associated with this item. |
|||