Some extreme forms defined in terms of Abelian groups

Abstract

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