Geodesic
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.

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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. 
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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/

[1] Minkowski H., Geometrie der Zahlen, Teubner, Lepzig–Berlin, 1910

[2] Minkowski H., Diophantische Approximationen, Teubner, Lepzig–Berlin, 1907 | Zbl

[3] Shmidt V., Diofantovy priblizheniya, Mir, M., 1983 | MR