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A035307 a(n)=least integer such that every even unimodular lattice in dimension 8n contains some vectors of all even (squared) norm >= 2*a(n). 0
0, 0, 2, 2, 2, 3 (list; graph; refs; listen; history; internal format)
OFFSET

1,3

COMMENTS

a(4) and a(5) are determined by Odlyzko and Sloane, a(6) by Peters and Kok Seng Chua gives an explicit upper bound for all a(n). Also both a(7) and a(8) are either 2 or 3 as established by Chakraborty et al.

REFERENCES

K. Chakraborty, A. K. Lal and B. Ramakrishnan, Modular forms that behave like theta series, Math. Computation, Vol. 66, 219, Jul 15 1997, pp. 1169-1183

Kok Seng Chua, An explicit Hecke's bound and exceptions of even unimodular quadratic forms, Bull. Austral. Math. Soc. 65 (2002), 231-238.

A. M. Odlyzko and N. J. A. Sloane, On exceptions of integral quadratic forms, J. reine angew Math. 321, 212-216, (1981)

M. Peters, Definite Unimodular 48-Dimensional Quadratic Forms, Bull. London Math. Soc., 15 (1983), 18-20

EXAMPLE

a(3)=2 because Leech lattice has no vectors of norm 2. All other 24-dimensional Niemeier lattices contains vectors of all even norms.

CROSSREFS

Sequence in context: A084954 A049300 A084957 * A004481 A004489 A112599

Adjacent sequences:  A035304 A035305 A035306 * A035308 A035309 A035310

KEYWORD

hard,nonn

AUTHOR

Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), May 25 2000

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Last modified February 17 13:28 EST 2012. Contains 206031 sequences.