REPRESENTATIONS OF POSITIVE-DEFINITE QUADRATIC-FORMS WITH CONGRUENCE AND PRIMITIVE CONDITIONS

Let M be a positive definite Z-lattice of rank m greater-than-or-equal-to 2n + 3 and let T be a finite set of primes containing 2 and those primes p for which M(p) 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 f:N --> M so that f approximates given local representations at T and so that f(N(p)) is primitive in M(p) for all primes p not member T or {q} where q is any fixed prime not in T. (C) 1994 Academic Press, Inc.