Universal Z-lattices of Minimal Rank

  title={Universal Z-lattices of Minimal Rank},
  author={OH BYEONG-KWEON},
  • Published 1999
Let UZ(n) be the minimal rank of n-universal Z-lattices, by which we mean positive definite Z-lattices which represent all positive Z-lattices of rank n. It is a well known fact that UZ(n) = n + 3 for 1 ≤ n ≤ 5. In this paper, we determine UZ(n) and find all n-universal lattices of rank UZ(n) for 6 ≤ n ≤ 8.