Representations of Positive Definite Quadratic Forms with Congruence and Primitive Conditions, II Original Research Article

Let M be a positive definite quadratic Z-module of rank m ≥ 7 and T a finite set of primes containing 2 and those primes p for which Mp is not unimodular. If N is a quadratic Z-module of rank 2 which is locally represented by M and if min(N) is sufficiently large then there exists a representation ƒ: N → M so that ƒ approximates given local representations at T and ƒ(Np) is primitive in Mp for all primes p negated set membership T.