Journal of the Australian Mathematical Society

Research Article

Some extreme forms defined in terms of Abelian groups

E. S. Barnesa1 and G. E. Walla1

a1 The University of Sydney.

Let S1446788700025064_inline1 be a positive definite quadratic form of determinant D, and let M be the minimum of f(x) for integral x ≠ 0. Then we set

S1446788700025064_eqn1

and
S1446788700025064_eqn2

the maximum being over all positive forms f in n variables. f is said to be extreme if y γn(f) is a local maximum for varying f, absolutely extreme if y γ(f) is an absolute maximum, i.e. if y γ(f) = γn.

(Received January 15 1959)