1-Universal binary and ternary Hermitian lattices over imaginary quadratic fields

Abstract

A positive definite Hermitian lattice is said to be 1-universal if it represents all positive definite unary Hermitian lattices, including both free and non-free Hermitian lattices. This paper is more concerned with the representations of unary non-free Hermitian lattices by Hermitian lattices. We estimate the minimal rank $$u_m^1$$ of 1-universal Hermitian lattices and we classify all 1-universal binary and ternary Hermitian lattices over imaginary quadratic fields $$\mathbb {Q}(\sqrt{-m})$$ for all positive square-free integers m.