Matematičeskie zametki, Tome 23 (1978) no. 6, pp. 789-797
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K. Bakiev; A. S. Pen; B. F. Skubenko. Upper bound for the product of nonhomogeneous linear forms. Matematičeskie zametki, Tome 23 (1978) no. 6, pp. 789-797. http://geodesic.mathdoc.fr/item/MZM_1978_23_6_a1/
@article{MZM_1978_23_6_a1,
author = {K. Bakiev and A. S. Pen and B. F. Skubenko},
title = {Upper bound for the product of nonhomogeneous linear forms},
journal = {Matemati\v{c}eskie zametki},
pages = {789--797},
year = {1978},
volume = {23},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_6_a1/}
}
TY - JOUR
AU - K. Bakiev
AU - A. S. Pen
AU - B. F. Skubenko
TI - Upper bound for the product of nonhomogeneous linear forms
JO - Matematičeskie zametki
PY - 1978
SP - 789
EP - 797
VL - 23
IS - 6
UR - http://geodesic.mathdoc.fr/item/MZM_1978_23_6_a1/
LA - ru
ID - MZM_1978_23_6_a1
ER -
%0 Journal Article
%A K. Bakiev
%A A. S. Pen
%A B. F. Skubenko
%T Upper bound for the product of nonhomogeneous linear forms
%J Matematičeskie zametki
%D 1978
%P 789-797
%V 23
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_1978_23_6_a1/
%G ru
%F MZM_1978_23_6_a1
It is proved that for any unimodular lattice $\Lambda$ with homogeneous minimum $L>0$ and any set of real numbers $\alpha_1,\alpha_2,\dots,\alpha_n$ there exists a point ($y_1, y_2,\dots,y_n$) of $\Lambda$ such that $$ \prod_{1\le i\le n}|y_i+\alpha_i|\le2^{-n/2_\gamma n}(1+3L^{8/(3^n)/(\gamma^{2/3}-2L^{8/(3^n)})})^{-n/2}, $$ where $\gamma^n=n^{n/(n-1)}$.
