Universal ℤ-lattices of minimal rank
Byeong-Kweon Oh · Proceedings of the American Mathematical Society · 1999
Let U Z ( n ) U_{\mathbb {Z}}(n) be the minimal rank of n n -universal Z \mathbb {Z} -lattices, by which we mean positive definite Z \mathbb {Z} -lattices which represent all positive Z \mathbb {Z} -lattices of rank n n . It is a well known fact that U Z ( n ) = n + 3 U_{\mathbb {Z}}(n)=n+ 3 for 1 ≤ n ≤ 5 1 \le n \le 5 . In this paper, we determine U Z ( n ) U_{\mathbb {Z}}(n) and find all n n -universal lattices of rank U Z ( n ) U_{\mathbb {Z}}(n) for 6 ≤