Geodesic
A new construction in the theory of lattice coverings of an $n$-dimensional space by equal spheres
Izvestiya. Mathematics , Tome 4 (1970) no. 2, pp. 293-302.

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

This article furnishes a new construction principle in the theory of lattice coverings of an $n$-dimensional space by equal spheres. The principle is based on the convexity of a body $\mathbf V$ in the parameter space. The whole theory is deduced from association of this convexity with strict convexity of the discriminant body. 
@article{IM2_1970_4_2_a1,
     author = {B. N. Delone and N. P. Dolbilin and S. S. Ryshkov and M. I. Shtogrin},
     title = {A new construction in the theory of lattice coverings of an $n$-dimensional space by equal spheres},
     journal = {Izvestiya. Mathematics },
     pages = {293--302},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1970_4_2_a1/}
}
TY  - JOUR
AU  - B. N. Delone
AU  - N. P. Dolbilin
AU  - S. S. Ryshkov
AU  - M. I. Shtogrin
TI  - A new construction in the theory of lattice coverings of an $n$-dimensional space by equal spheres
JO  - Izvestiya. Mathematics 
PY  - 1970
SP  - 293
EP  - 302
VL  - 4
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1970_4_2_a1/
LA  - en
ID  - IM2_1970_4_2_a1
ER  - 
%0 Journal Article
%A B. N. Delone
%A N. P. Dolbilin
%A S. S. Ryshkov
%A M. I. Shtogrin
%T A new construction in the theory of lattice coverings of an $n$-dimensional space by equal spheres
%J Izvestiya. Mathematics 
%D 1970
%P 293-302
%V 4
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1970_4_2_a1/
%G en
%F IM2_1970_4_2_a1
B. N. Delone; N. P. Dolbilin; S. S. Ryshkov; M. I. Shtogrin. A new construction in the theory of lattice coverings of an $n$-dimensional space by equal spheres. Izvestiya. Mathematics , Tome 4 (1970) no. 2, pp. 293-302. http://geodesic.mathdoc.fr/item/IM2_1970_4_2_a1/

[1] Weyl H., “Über die Gleichverteilung von Zahlen mod. Eins”, Math. Ann., 77:3 (1916), 313–352 | DOI | MR | Zbl

[2] Rogers C. A., Packing and Covering, Cambridge University Press, Cambridge, 1964 | MR

[3] Bambah R. P., “On lattice covering by spheres”, Proc. Nat. Inst. Sci. India, 20 (1954), 25–52 | MR | Zbl

[4] Gametskii A. F., “Ob optimalnosti glavnoi reshetki pervogo tipa Voronogo sredi reshetok pervogo tipa lyubogo chisla izmerenii”, Dokl. AN SSSR, 151:3 (1963), 482–484 | Zbl

[5] Delone B. N., Ryshkov S. S., “Reshenie zadachi o naimenee plotnom reshetchatom pokrytii chetyrekhmernogo prostranstva ravnymi sharami”, Dokl. AN SSSR, 152:3 (1963), 523–524 | MR | Zbl

[6] Ryshkov S. S., “Nekotorye zamechaniya o tipakh $n$-mernykh paralleloedrov i o plotnosti reshetchatykh pokrytii prostranstva $E^N$ raznymi sharami”, Dokl. AN SSSR, 162:2 (1965), 277–280 | Zbl

[7] Ryshkov S. S., “Effektizatsiya odnogo metoda Davenporta v teorii pokrytii”, Dokl. AN SSSR, 175:2 (1967), 303–306

[8] Baranovskii E. P., “Lokalnye minimumy plotnosti reshetchatogo pokrytiya chetyrekhmernogo evklidova prostranstva ravnymi sharami”, Dokl. AN SSSR, 164:1 (1965), 13–15 | MR | Zbl

[9] Baranovskii E. P., Ryshkov S. S., “O vtorom lokalnom minimume plotnosti reshetchatogo pokrytiya chetyrekhmernogo prostranstva ravnymi sharami”, Sib. matem. zh., 7:4 (1966), 731–739 | MR | Zbl

[10] Baranovskii E. P., “Lokalnye minimumy plotnosti reshetchatogo pokrytiya evklidova prostranstva ravnymi sharami”, Sib. matem. zh., 7:5 (1966), 974–1001 | MR | Zbl

[11] Baranovskii E. P., “Ob ekstremalnykh reshetchatykh pokrytiyakh”, Uch. zap. Ivanovsk. gos. ped. in-ta, 44, 1969, 47–57 | MR

[12] Barnes E. S., Dickson T. J., “Extreme coverings of $n$-space by spheres”, J. Austr. Math. Soc., VII:1 (1967), 115–127 | DOI | MR

[13] Dickson T. J., “The extreme covering of 4-space by spheres”, J. Austr. Math. Soc., VII:4 (1967), 490–496 | DOI | MR

[14] Dickson T. J., “A sufficient condition for an extreme covering on $n$-space by spheres”, J. Austr. Math. Soc., VIII:1 (1968), 56–62 | DOI | MR

[15] Delone B. N., “Geometriya polozhitelnykh kvadratichnykh form”, Uspekhi matem. nauk, 1937, no. 3, 16–62

[16] Minkowski H., “Diskontinuitätsbereich für arithmetiche Aequivalenz”, J. reine und angew. Math., 129 (1905), 220–274

[17] Voronoi G. F., Sobranie sochinenii v trekh tomakh, t. 2, AN USSR, Kiev, 1952, 171–238