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

Let M be a positive definite Z-lattice of rank m ≥ 2n + 3 and let T be a finite set of primes containing 2 and those primes p for which Mp is not unimodular. If N is a lattice of rank n 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 so that ƒ(Np) is primitive in Mp for all primes p negated set membership T union or logical sum {q} where q is any fixed prime not in T.