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.

中文翻译：

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虚二次域上的1-通用二元和三元Hermitian格

如果正定性Hermitian格表示所有正定一元Hermitian格，包括自由和非自由Hermitian格，则称其为1通用。本文更关注用Hermitian格表示一元非自由Hermitian格。我们估计1个通用Hermitian晶格的最小秩\（u_m ^ 1 \），并在虚二次域\（\ mathbb {Q}（\ sqrt {-m}）\\上对所有1个Universal二元和三元Hermitian晶格进行分类。 ）对于所有正无平方整数m。