Geodesic
On simultaneous Diophantine approximations. Vectors of given Diophantine type
Matematičeskie zametki, Tome 61 (1997) no. 5, pp. 706-716.

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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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     author = {N. G. Moshchevitin},
     title = {On simultaneous {Diophantine} approximations. {Vectors} of given {Diophantine} type},
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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/

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