Representations by integral quadratic forms

AbstractLet M and N be lattices on regular quadratic spaces over an algebraic number field and N(M, N) the number of essentially distinct primitive representations of N by M. Conditions are given under which N(M, N) can be expressed as a product of the corresponding local representation numbers N(Mp, Np). The related problem of extending an isometry between two regular sublattices of M to an element in the group of units of M is also considered