Representations of Positive Definite Hermitian Forms with Approximation and Primitive Properties Original Research Article

Let M be a positive definite hermitian lattice of rank m ≥ 2n + 1 and T be a finite set of primes containing the prime divisors of 2 vol(M). If N is a hermitian lattice of rank n which is locally representable by M and min(N) is sufficiently large, then there exists a global representation ƒ: N → M such that ƒ approximates the given local representations at T and 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.