Trudy Instituta matematiki, Tome 15 (2007) no. 1, pp. 10-14
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D. V. Vasilyev; D. V. Koleda. Minkowski's theorem on successive minima and its application to metric Diophantine approximation theory. Trudy Instituta matematiki, Tome 15 (2007) no. 1, pp. 10-14. http://geodesic.mathdoc.fr/item/TIMB_2007_15_1_a1/
@article{TIMB_2007_15_1_a1,
author = {D. V. Vasilyev and D. V. Koleda},
title = {Minkowski's theorem on successive minima and its application to metric {Diophantine} approximation theory},
journal = {Trudy Instituta matematiki},
pages = {10--14},
year = {2007},
volume = {15},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMB_2007_15_1_a1/}
}
TY - JOUR
AU - D. V. Vasilyev
AU - D. V. Koleda
TI - Minkowski's theorem on successive minima and its application to metric Diophantine approximation theory
JO - Trudy Instituta matematiki
PY - 2007
SP - 10
EP - 14
VL - 15
IS - 1
UR - http://geodesic.mathdoc.fr/item/TIMB_2007_15_1_a1/
LA - ru
ID - TIMB_2007_15_1_a1
ER -
%0 Journal Article
%A D. V. Vasilyev
%A D. V. Koleda
%T Minkowski's theorem on successive minima and its application to metric Diophantine approximation theory
%J Trudy Instituta matematiki
%D 2007
%P 10-14
%V 15
%N 1
%U http://geodesic.mathdoc.fr/item/TIMB_2007_15_1_a1/
%G ru
%F TIMB_2007_15_1_a1
We give upper and lower bounds for the volumes of the bodies given by the system of linear inequalities in $\mathbb C\times\mathbb R$. As a consequences we get an analogue of Minkowski theorem on consequtive minima and the theorem on joint approximation of zero by the values of polynomials in complex and real points.
