Some extreme forms defined in terms of Abelian groups

摘要

Let be a positive definite quadratic form of determinant D, and let M be the minimum of f(x) for integral x a‰? 0. Then we set and the maximum being over all positive forms f in n variables. f is said to be extreme if y ?3n(f) is a local maximum for varying f, absolutely extreme if y ?3(f) is an absolute maximum, i.e. if y ?3(f) = ?3n.