Geodesic
Estimats of the inhomogeneous arithmetical minimum of the product of linear forms
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 8, Tome 160 (1987), pp. 138-150

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Further refinements of Chebotarev type estimates are obtained for the inhomogeneous arithmetic minimum $M_n$ of a lattice $\Lambda$ of determinant $d(\Lambda)$ in the inhomogeneous Minkowski conjecture. In particular, it is proved that for every $n_0\geq2$ there exists an effectively computed constant $c=c(n_0)$ for which $$ M_n\leq2^{-n/2}(cn^{-1/2}\log^{1/2}n)d(\Lambda). $$ 
@article{ZNSL_1987_160_a12,
     author = {A. V. Malyshev},
     title = {Estimats of the inhomogeneous arithmetical minimum of the product of linear forms},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {138--150},
     publisher = {mathdoc},
     volume = {160},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a12/}
}
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A. V. Malyshev. Estimats of the inhomogeneous arithmetical minimum of the product of linear forms. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 8, Tome 160 (1987), pp. 138-150. http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a12/