메뉴 건너뛰기




Volumn 10, Issue 7, 2004, Pages 58-67

The densest lattice in twenty-four dimensions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 15944409994     PISSN: None     EISSN: 10796762     Source Type: Journal    
DOI: 10.1090/S1079-6762-04-00130-1     Document Type: Article
Times cited : (33)

References (17)
  • 1
    • 0001732343 scopus 로고
    • The complete enumeration of extreme senary forms
    • MR 0086833 (19:251d)
    • E. S. Barnes, The complete enumeration of extreme senary forms, Phil. Transact. Royal Soc. London A 249 (1957), 461-506. MR 0086833 (19:251d)
    • (1957) Phil. Transact. Royal Soc. London A , vol.249 , pp. 461-506
    • Barnes, E.S.1
  • 2
    • 0040933747 scopus 로고
    • The minimum values of positive quadratic forms in six, seven and eight variables
    • H. F. Blichfeldt, The minimum values of positive quadratic forms in six, seven and eight variables, Math. Z. 39 (1935), 1-15.
    • (1935) Math. Z , vol.39 , pp. 1-15
    • Blichfeldt, H.F.1
  • 3
    • 0037909703 scopus 로고    scopus 로고
    • New upper bounds on sphere packings II
    • arXiv:math.MG/0110010. MR 1914571 (2004b:52032)
    • H. Cohn, New upper bounds on sphere packings II, Geom. Topol. 6 (2002), 329-353, arXiv:math.MG/0110010. MR 1914571 (2004b:52032)
    • (2002) Geom. Topol , vol.6 , pp. 329-353
    • Cohn, H.1
  • 4
    • 0037769863 scopus 로고    scopus 로고
    • New upper bounds on sphere packings I
    • arXiv:math.MG/0110009. MR 1973059 (2004b:11096)
    • H. Cohn and N. Elkies, New upper bounds on sphere packings I, Annals of Mathematics 157 (2003), 689-714, arXiv:math.MG/0110009. MR 1973059 (2004b:11096)
    • (2003) Annals of Mathematics , vol.157 , pp. 689-714
    • Cohn, H.1    Elkies, N.2
  • 5
    • 85009821994 scopus 로고    scopus 로고
    • preprint, arXiv:math.MG/0403263
    • H. Cohn and A. Kumar, Optimality and uniqueness of the Leech lattice among lattices, preprint, 2003, arXiv:math.MG/0403263.
    • (2003)
    • Cohn, H.1    Kumar, A.2
  • 7
    • 65649140960 scopus 로고
    • Spherical codes and designs
    • MR 0485471 (58:5302)
    • P. Delsarte, J. Goethals, and J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363-388. MR 0485471 (58:5302)
    • (1977) Geometriae Dedicata , vol.6 , pp. 363-388
    • Delsarte, P.1    Goethals, J.2    Seidel, J.3
  • 8
    • 15944421702 scopus 로고    scopus 로고
    • Lattices, linear codes, and invariants
    • 1382-1391. MR 1784239 (2001g:11110)
    • N. Elkies, Lattices, linear codes, and invariants, Notices Amer. Math. Soc. 47 (2000), 1238-1245 and 1382-1391. MR 1784239 (2001g:11110)
    • (2000) Notices Amer. Math. Soc , vol.47 , pp. 1238-1245
    • Elkies, N.1
  • 9
    • 0347551990 scopus 로고
    • Untersuchungen über die Eigenschaften der positiven ternären quadratischen Formen von Ludwig August Seeber
    • July 9, Reprinted in Werke, Vol. 2, Königliche Gesellschaft der Wissenschaften, Göttingen, 1863, Available from the Göttinger Digitalisierungszentrum
    • C. F. Gauss, Untersuchungen über die Eigenschaften der positiven ternären quadratischen Formen von Ludwig August Seeber, Göttingische gelehrte Anzeigen, July 9, 1831. Reprinted in Werke, Vol. 2, Königliche Gesellschaft der Wissenschaften, Göttingen, 1863, 188-196. Available from the Göttinger Digitalisierungszentrum at http://gdz.sub.uni-goettingen.de.
    • (1831) Göttingische Gelehrte Anzeigen , pp. 188-196
    • Gauss, C.F.1
  • 10
    • 0004019764 scopus 로고
    • second edition, Elsevier Science Publishers, MR 0893813 (88j:11034)
    • P. Gruber and C. Lekkerkerker, Geometry of Numbers, second edition, Elsevier Science Publishers, 1987. MR 0893813 (88j:11034)
    • (1987) Geometry of Numbers
    • Gruber, P.1    Lekkerkerker, C.2
  • 11
    • 0000836432 scopus 로고
    • Sur les formes quadratiques
    • A. Korkine and G. Zolotareff, Sur les formes quadratiques, Math. Ann. 6 (1873), 366-389.
    • (1873) Math. Ann , vol.6 , pp. 366-389
    • Korkine, A.1    Zolotareff, G.2
  • 12
    • 0040156836 scopus 로고
    • Sur les formes quadratiques positives
    • A. Korkine and G. Zolotareff, Sur les formes quadratiques positives, Math. Ann. 11 (1877), 242-292.
    • (1877) Math. Ann , vol.11 , pp. 242-292
    • Korkine, A.1    Zolotareff, G.2
  • 13
    • 0038247240 scopus 로고
    • On bounds for packings in n-dimensional Euclidean space
    • MR 0529659 (80d:52017)
    • V. I. Levenshtein, On bounds for packings in n-dimensional Euclidean space, SovietMathematics Doklady 20 (1979), 417-421. MR 0529659 (80d:52017)
    • (1979) Sovietmathematics Doklady , vol.20 , pp. 417-421
    • Levenshtein, V.I.1
  • 15
    • 0001179224 scopus 로고
    • New bounds on the number of unit spheres that can touch a unit sphere in n dimensions
    • MR 0530296 (81d:52010)
    • A. M. Odlyzko and N. J. A. Sloane, New bounds on the number of unit spheres that can touch a unit sphere in n dimensions, Journal of Combinatorial Theory A 26 (1979), 210-214. MR 0530296 (81d:52010)
    • (1979) Journal of Combinatorial Theory A , vol.26 , pp. 210-214
    • Odlyzko, A.M.1    Sloane, N.J.A.2
  • 16
    • 15944412759 scopus 로고
    • Uniqueness of classes of positive quadratic forms on which values of the Hermite constant are attained for 6 ≤ n ≤ 8, in Geometry of positive quadratic forms
    • N. M. Vetčinkin, Uniqueness of classes of positive quadratic forms on which values of the Hermite constant are attained for 6 ≤ n ≤ 8, in Geometry of positive quadratic forms, Trudy Math. Inst. Steklov. 152 (1980), 34-86
    • (1980) Trudy Math. Inst. Steklov , vol.152 , pp. 34-86
    • Vetčinkin, N.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.