Geodesic
To the Blichfeldt--Mullender--Spohn Theorem on Simultaneous Approximation
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Discrete geometry and geometry of numbers, Tome 239 (2002), pp. 268-274

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A new approach to strengthening a result of Spohn based on the analysis of best approximations is suggested. Let $\alpha _1,\dots ,\alpha _m$ be real numbers. Let $c_m$ denote the least upper bound of all constants $\sigma $ for which the inequality $\max _{j=1,\dots ,m}\|p\alpha _j\| (\sigma p)^{-1/m}$ has infinitely many positive integer solutions $p$; here, $\|\cdot \|$ is the distance to the nearest integer. Lower bounds for $c_m$ that hold for all $m$ are studied. 
@article{TM_2002_239_a16,
     author = {N. G. Moshchevitin},
     title = {To the {Blichfeldt--Mullender--Spohn} {Theorem} on {Simultaneous} {Approximation}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {268--274},
     publisher = {mathdoc},
     volume = {239},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2002_239_a16/}
}
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N. G. Moshchevitin. To the Blichfeldt--Mullender--Spohn Theorem on Simultaneous Approximation. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Discrete geometry and geometry of numbers, Tome 239 (2002), pp. 268-274. http://geodesic.mathdoc.fr/item/TM_2002_239_a16/