Exponents of Diophantine Approximation in dimension two
| dc.creator | Laurent, Michel | |
| dc.date | 2006-11-12 | |
| dc.date.accessioned | 2026-07-07T07:32:48Z | |
| dc.date.available | 2026-07-07T07:32:48Z | |
| dc.description | Let $Θ=(α,β)$ be a point in $\bR^2$, with $1,α,β$ linearly independent over $\bQ$. We attach to $Θ$ a quadruple $Ω(Θ)$ of exponents which measure the quality of approximation to $Θ$ both by rational points and by rational lines. The two ``uniform'' components of $Ω(Θ)$ are related by an equation, due to Jarn{\'ı}k, and the four exponents satisfy two inequalities which refine Khintchine's transference principle. Conversely, we show that for any quadruple $Ω$ fulfilling these necessary conditions, there exists a point $Θ\in \bR^2$ for which $Ω(Θ) =Ω$. | |
| dc.identifier | https://arxiv.org/abs/math/0611352 | |
| dc.identifier | http://arxiv.org/abs/math/0611352 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119241 | |
| dc.subject | Number Theory | |
| dc.subject | 11J13; 11J70 | |
| dc.title | Exponents of Diophantine Approximation in dimension two | |
| dc.type | text |