On inhomogeneous diophantine approximation with some quasi-periodic expressions, II

Komatsu, Takao

Journal de théorie des nombres de Bordeaux, Tome 11 (1999) no. 2, pp. 331-344

Abstract (VO)

We consider the values concerning

$$ℳ(\theta ,\phi )=\underset{\left|q\right|\to \infty }{lim\; inf}\left|q\right|\left|\right|q^{\theta }-\phi \left|\right|$$

where the continued fraction expansion of $\theta$ has a quasi-periodic form. In particular, we treat the cases so that each quasi-periodic form includes no constant. Furthermore, we give some general conditions satisfying $ℳ(\theta ,\phi )=0$.

Résumé

On s’intéresse aux valeurs de

$$ℳ(\theta ,\phi )=\underset{\left|q\right|\to \infty }{lim\; inf}\left|q\right|\left|\right|q^{\theta }-\phi \left|\right|$$

lorsque $\theta$ est un réel ayant un développement en fraction continue quasi-périodique.