On Indecomposable Definite Hermitian Forms  

作　　者：Zhu Fuzu 

机构地区：[1]Department of Mathematics East China Normal University Shanghai

出　　处：《Acta Mathematica Sinica,English Series》1995年第3期291-299,共9页数学学报（英文版）

摘　　要：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(-3^1/2) 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_m-lattices of any given rank n and discriminant a, where R_m is the ring of algebraic integers in an imaginary quadratic field Q(-m^1/2) with class number unity.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(-3^1/2) 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_m-lattices of any given rank n and discriminant a, where R_m is the ring of algebraic integers in an imaginary quadratic field Q(-m^1/2) with class number unity.

关 键 词：Indecomposable lattics (form) Unimodular lattice (form) Minimum of a lattice Irreducible vector 

分 类 号：O1[理学—数学]