Geodesic
The product of linear nonhomogeneous forms
Matematičeskie zametki, Tome 16 (1974) no. 3, pp. 365-374 
Kh. N. Narzullaev. The product of linear nonhomogeneous forms. Matematičeskie zametki, Tome 16 (1974) no. 3, pp. 365-374. http://geodesic.mathdoc.fr/item/MZM_1974_16_3_a1/
@article{MZM_1974_16_3_a1,
     author = {Kh. N. Narzullaev},
     title = {The product of linear nonhomogeneous forms},
     journal = {Matemati\v{c}eskie zametki},
     pages = {365--374},
     year = {1974},
     volume = {16},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_3_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We show that for an arbitrary unimodular lattice $\Lambda$ of dimension $n$ and an arbitrary point $C=(c_1,c_2,\dots,c_n)\in R^n$ a point $Y=(y_1,y_2,\dots,y_n)\in\Lambda$ can be found and also a number h, satisfying the condition $1\le h\le2^{-n/2}\theta^{-1}+1$ ($0<\theta\le2^{-n/2}$), such that the inequality $$ \prod_{i=1}^n|y_i+hc_i|<\theta $$ will be satisfied.