Low-dimensional lattices. IV. The mass formula

Abstract

The mass formula expresses the sum of the reciprocals of the group orders of the lattices in a genus in terms of the properties of any of them. We restate the formula so as to make it easier to compute. In particular we give a simple and reliable way to evaluate the 2-adic contribution. Our version, unlike earlier ones, is visibly invariant under scale changes and dualizing. We use the formula to check the enumeration of lattices of determinant d ≼ 25 given in the first paper in this series. We also give tables of the ‘standard mass’, the L -series Σ( n / m ) m -s ( m odd), and genera of lattices of determinant d ≼ 25.