Geodesic
The defect of an admissible octahedron in a~lattice
Matematičeskie zametki, Tome 58 (1995) no. 4, pp. 558-568.

Voir la notice de l'article provenant de la source Math-Net.Ru

Systems of vectors determining an admissible octahedron in a lattice are considered. We discuss the property that such a system may be complemented to a basis of this lattice. 
@article{MZM_1995_58_4_a7,
     author = {N. G. Moshchevitin},
     title = {The defect of an admissible octahedron in a~lattice},
     journal = {Matemati\v{c}eskie zametki},
     pages = {558--568},
     publisher = {mathdoc},
     volume = {58},
     number = {4},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a7/}
}
TY  - JOUR
AU  - N. G. Moshchevitin
TI  - The defect of an admissible octahedron in a~lattice
JO  - Matematičeskie zametki
PY  - 1995
SP  - 558
EP  - 568
VL  - 58
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a7/
LA  - ru
ID  - MZM_1995_58_4_a7
ER  - 
%0 Journal Article
%A N. G. Moshchevitin
%T The defect of an admissible octahedron in a~lattice
%J Matematičeskie zametki
%D 1995
%P 558-568
%V 58
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a7/
%G ru
%F MZM_1995_58_4_a7
N. G. Moshchevitin. The defect of an admissible octahedron in a~lattice. Matematičeskie zametki, Tome 58 (1995) no. 4, pp. 558-568. http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a7/

[1] Rankin R. A., “On Sums of Powers of Linear Forms, III”, Indag. Math., 10 (1949), 274–281

[2] Blichfeldt H. F., “A New Upper Bound to the Minimum Value of the Sum of Homogeneous Linear Forms”, Monatsh. Math., 43 (1936), 410–414 | DOI | Zbl

[3] Kassels Dzh. V. S., Vvedenie v geometriyu chisel, Mir, M., 1965

[4] Gruber P. M., Lekkerkerker C. G., Geometry of Numbers, Amsterdam, 1987

[5] Korobov N. M., “O nekotorykh voprosakh teorii diofantovykh priblizhenii”, UMN, 22:3 (1967), 83–118 | MR | Zbl

[6] Cusick T. W., Wolfskill J., “Lattice Octaedra and Sums of Powers of Linear Forms”, J. London Math. Soc. (2), 38 (1988), 207–215 | DOI | MR | Zbl

[7] Moschevitin N. G., “Utochnenie otsenki indeksa v probleme oktaedra”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1993, no. 6 | Zbl

[8] Mordell L. J., “Lattice octaedra”, Canad. J. Math., 12 (1960), 297–302 | MR | Zbl

[9] Bantegnie R., “Le probleme des octaedres en dimension 5”, Acta Arithm., 14 (1968), 185–202 | MR | Zbl

[10] Wessels U., Die Sätze von white und Mordell über kritische hitter von polytopen in der dimensionen 4 und 5, Preprint. Diplomarbeit, Mathematisches Institute der Ruhr-Universität Bochum, 1989