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A169719 Theta series of extremal lattice of dimension 14, level 7 and minimal norm 6. 0

%I #1 Jun 01 2010 03:00:00

%S 1,0,0,560,2394,9072,26824,71136,158004,306432,599256,1034208,1784328,

%T 2849616,4489776,6664896,9985374,14200704

%N Theta series of extremal lattice of dimension 14, level 7 and minimal norm 6.

%C The lattice has Gram matrix:

%C 6

%C -2 6

%C 2 -3 6

%C -3 0 1 6

%C -3 1 -2 3 6

%C -1 3 0 2 0 6

%C -1 2 -3 1 3 2 6

%C 2 -2 0 -3 -3 -3 -3 6

%C -3 3 -1 1 1 3 0 -1 6

%C 2 1 0 0 -2 1 1 1 -2 6

%C -2 3 0 1 2 2 2 -3 1 -1 6

%C -3 3 0 2 1 2 -1 -1 2 0 2 6

%C -3 3 -3 1 3 2 3 -2 3 0 1 2 6

%C 2 1 2 -2 -1 1 0 -1 1 -1 1 0 -1 6

%D Scharlau, Rudolf and Schulze-Pillot, Rainer, Extremal lattices, in Algorithmic algebra and number theory (Heidelberg, 1997), 139-170, Springer, Berlin, 1999. [Here the existence of such a lattice is left open.]

%e 1 + 560*q^3 + 2394*q^4 + 9072*q^5 + 26824*q^6 + 71136*q^7 + 158004*q^8 + 306432*q^9 + 599256*q^10 + 1034208*q^11 + 1784328*q^12 + 2849616*q^13 + 4489776*q^14 + 6664896*q^15 + 9985374*q^16 + 14200704*q^17 + O(q^18)

%K nonn

%O 0,4

%A Boris Hemkemeier (bhemkemeier(AT)googlemail.com) and Rudolf Scharlau (Rudolf.Scharlau(AT)math.uni-dortmund.de), Apr 21 2010

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)