Mathematika

Research Article

Extremal self-dual lattices exist only in dimensions 1 to 8, 12, 14, 15, 23, and 24

J. H. Conwaya1, A. M. Odlyzkoa2 and N. J. A. Sloanea2

a1 University of Cambridge, Cambridge, England.

a2 Bell Laboratories, Murray Hill, New Jersey, 07974, U.S.A

Abstract

It is known that if Λ is a self-dual lattice in n, then

S0025579300009244_eqnU1

.

If equality holds the lattice is called extremal. In this paper we find all the extremal lattices: there are unique lattices in dimensions 1, 2, 3, 4, 5, 6, 7, 8, 12, 14, 15, 23, 24 and no others.

(Received July 15 1977)

Key Words:

  • 10E25: NUMBER THEORY; Geometry of Numbers; Quadratic forms