Geodesic
On simultaneous Diophantine approximations. Vectors of given Diophantine type
Matematičeskie zametki, Tome 61 (1997) no. 5, pp. 706-716 
N. G. Moshchevitin. On simultaneous Diophantine approximations. Vectors of given Diophantine type. Matematičeskie zametki, Tome 61 (1997) no. 5, pp. 706-716. http://geodesic.mathdoc.fr/item/MZM_1997_61_5_a7/
@article{MZM_1997_61_5_a7,
     author = {N. G. Moshchevitin},
     title = {On simultaneous {Diophantine} approximations. {Vectors} of given {Diophantine} type},
     journal = {Matemati\v{c}eskie zametki},
     pages = {706--716},
     year = {1997},
     volume = {61},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_5_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

For any monotone function $\psi(y)=O(y^{-1/s})$, we prove the existence of a continual family of vectors $(\alpha_1,\dots,\alpha_s)\in\mathbb R^s$ admitting infinitely many simultaneous $\psi$-approximations, but no $c\psi$-approximations with some constant $c>0$.

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