In this paper, for any given natural numbers n and a, we can construct explicitly positive definite indecomposable integral Hermitian forms of rank n over Q(-3<sup>1/2</sup>) with discriminant a, with the ...In this paper, for any given natural numbers n and a, we can construct explicitly positive definite indecomposable integral Hermitian forms of rank n over Q(-3<sup>1/2</sup>) with discriminant a, with the following ten exceptions: n=2, a=1,2,4, 10; n=3, a=1,2,5; n=4, a=1; n=5, a=1; and n=7, a=1. In the exceptional cases there are no forms with the desired properties. The method given here can be applied to solving the problem of constructing indecomposable positive definite Hermitian R<sub>m</sub>-lattices of any given rank n and discriminant a, where R<sub>m</sub> is the ring of algebraic integers in an imaginary quadratic field Q(-m<sup>1/2</sup>) with class number unity.展开更多
文摘In this paper, for any given natural numbers n and a, we can construct explicitly positive definite indecomposable integral Hermitian forms of rank n over Q(-3<sup>1/2</sup>) with discriminant a, with the following ten exceptions: n=2, a=1,2,4, 10; n=3, a=1,2,5; n=4, a=1; n=5, a=1; and n=7, a=1. In the exceptional cases there are no forms with the desired properties. The method given here can be applied to solving the problem of constructing indecomposable positive definite Hermitian R<sub>m</sub>-lattices of any given rank n and discriminant a, where R<sub>m</sub> is the ring of algebraic integers in an imaginary quadratic field Q(-m<sup>1/2</sup>) with class number unity.
