This Paper gives a method to construct indecomposable positive definite integral Hermitianforman imnginary quadratic field Q with gin discriminant and g。n rank.It is shown that for ally natural numbers n and a, there...This Paper gives a method to construct indecomposable positive definite integral Hermitianforman imnginary quadratic field Q with gin discriminant and g。n rank.It is shown that for ally natural numbers n and a, there are n-ary Indecomposable positivedefinite intopal Herlllltian lattices over Q(resp. Q)with discriminant a, exceptfor four(resp. one) exceptions. In these exceptional cases there are no lattices with the desiredproperties.展开更多
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
Let F=Q(i=m<sup>1/2</sup>（i<sup>2</sup>=-1, m】0 and square free） be an imaginary quadratic field and R<sub>m</sub> its ring of algebraic integers. The aim of this note is to cons...Let F=Q(i=m<sup>1/2</sup>（i<sup>2</sup>=-1, m】0 and square free） be an imaginary quadratic field and R<sub>m</sub> its ring of algebraic integers. The aim of this note is to construct n-ary positive definite indecomposable integral. Hermitian forms over R<sub>m</sub> with given rank and given discriminant. The word decomposition or splitting is the geometric one, i. e. lattice L has a non-trivial expression of the form L=M⊥N. If there is no such expression we call L indecomposable. There is another kind of decomposition——a more algebraic one. A positive definite Hermitian展开更多
文摘This Paper gives a method to construct indecomposable positive definite integral Hermitianforman imnginary quadratic field Q with gin discriminant and g。n rank.It is shown that for ally natural numbers n and a, there are n-ary Indecomposable positivedefinite intopal Herlllltian lattices over Q(resp. Q)with discriminant a, exceptfor four(resp. one) exceptions. In these exceptional cases there are no lattices with the desiredproperties.
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.
文摘Let F=Q(i=m<sup>1/2</sup>（i<sup>2</sup>=-1, m】0 and square free） be an imaginary quadratic field and R<sub>m</sub> its ring of algebraic integers. The aim of this note is to construct n-ary positive definite indecomposable integral. Hermitian forms over R<sub>m</sub> with given rank and given discriminant. The word decomposition or splitting is the geometric one, i. e. lattice L has a non-trivial expression of the form L=M⊥N. If there is no such expression we call L indecomposable. There is another kind of decomposition——a more algebraic one. A positive definite Hermitian
