Bulletin of the American Mathematical Society

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Book Information:

Author: J. H. Conway and N. J. A. Sloane
Title: Sphere packings, lattices and groups, second ed.
Additional book information: Grundlehren der Mathematischen Wissenschaften, bd.\ 290, Springer-Verlag, New York and Berlin, 1993, xliii+679 pp., US$69.00. ISBN 0-387-97912-3 and ISBN 3-540-97912-3.

H. F. Blichfeldt, A new principle in the geometry of numbers, with some applications, Trans. Amer. Math. Soc. 15 (1914), no. 3, 227–235. MR 1500976, DOI 10.1090/S0002-9947-1914-1500976-6

J. W. S. Cassels, An introduction to the geometry of numbers, Die Grundlehren der mathematischen Wissenschaften, Band 99, Springer-Verlag, Berlin-New York, 1971. Second printing, corrected. MR 0306130

H. S. M. Coxeter, L. Few, and C. A. Rogers, Covering space with equal spheres, Mathematika 6 (1959), 147–157. MR 124821, DOI 10.1112/S0025579300002059

[4]

L. Fejes Toth, Lagerungen in der Ebene, auf der Kugel und in Raum, Grundlehren Math. Wiss., bd. 65, Springer, Berlin, 1953.

[5]

-, Regular figures, Pergamon, Oxford, 1964.

L. Fejes Tóth, On the densest packing of convex discs, Mathematika 30 (1983), no. 1, 1–3. MR 720944, DOI 10.1112/S0025579300010354

P. M. Gruber and C. G. Lekkerkerker, Geometry of numbers, 2nd ed., North-Holland Mathematical Library, vol. 37, North-Holland Publishing Co., Amsterdam, 1987. MR 893813

Edmund Hlawka, Zur Geometrie der Zahlen, Math. Z. 49 (1943), 285–312 (German). MR 9782, DOI 10.1007/BF01174201

[9]

G. A. Kabatiansky and V. I. Levenshtein, Bounds for packings on a sphere and in space, Problems of Information Transmission 14 (1978), 1-17.

[10]

J. Kepler, The six-cornered snowflake, Translated from the Latin booklet of 1611 by Colin Hardie, Clarendon Press, Oxford, 1966.

[11]

H. Minkowski, Diphantische approximationen, Teubner, Leipzig, 1907.

[12]

-, Geometrie der Zahlen, Teubner, Leipzig, 1910.

[13]

-, Gesammelte abhandlungen, Teubner, Berlin, 1911.

C. A. Rogers, Existence theorems in the geometry of numbers, Ann. of Math. (2) 48 (1947), 994–1002. MR 22863, DOI 10.2307/1969390

C. A. Rogers, Packing and covering, Cambridge Tracts in Mathematics and Mathematical Physics, No. 54, Cambridge University Press, New York, 1964. MR 0172183

Carl Ludwig Siegel, A mean value theorem in geometry of numbers, Ann. of Math. (2) 46 (1945), 340–347. MR 12093, DOI 10.2307/1969027

[1]

H. F. Blichfeldt, A new principle in the geometry of numbers, Trans. Amer. Math. Soc. 15 (1914), 227-235. MR 1500976

[2]

J. W. S. Cassels, An introduction to the geometry of numbers, Springer-Verlag, New York, 1971. MR 0306130 (46:5257)

[3]

H. S. M. Coxeter, L. Few, and C. A. Rogers, Covering space with equal spheres, Mathematika 6 (1959), 147-157. MR 0124821 (23:A2131)

[4]

L. Fejes Toth, Lagerungen in der Ebene, auf der Kugel und in Raum, Grundlehren Math. Wiss., bd. 65, Springer, Berlin, 1953.

[5]

-, Regular figures, Pergamon, Oxford, 1964.

[6]

-, On the densest packing of convex discs, Mathematika 30 (1983), 1-3. MR 720944 (85e:52021)

[7]

P. M. Gruber and C. G. Lekkerkerker, Geometry of numbers, 2nd ed., North-Holland, Amsterdam, 1987. MR 893813 (88j:11034)

[8]

E. Hlawka, Zur Geometrie der Zahlen, Math. Z. 49 (1944), 285-312. MR 0009782 (5:201c)

[9]

G. A. Kabatiansky and V. I. Levenshtein, Bounds for packings on a sphere and in space, Problems of Information Transmission 14 (1978), 1-17.

[10]

J. Kepler, The six-cornered snowflake, Translated from the Latin booklet of 1611 by Colin Hardie, Clarendon Press, Oxford, 1966.

[11]

H. Minkowski, Diphantische approximationen, Teubner, Leipzig, 1907.

[12]

-, Geometrie der Zahlen, Teubner, Leipzig, 1910.

[13]

-, Gesammelte abhandlungen, Teubner, Berlin, 1911.

[14]

C. A. Rogers, Existence theorems in the geometry of numbers, Ann. of Math. (2) 48 (1947), 994-1002. MR 0022863 (9:270h)

[15]

-, Packing and covering, Cambridge Univ. Press, London and New York, 1964. MR 0172183 (30:2405)

[16]

C. L. Siegel, A mean value theorem in the geometry of numbers, Ann. of Math. (2) 46 (1945), 340-347. MR 0012093 (6:257b)