Methods are presented for the construction of nondecomposable positive definite integral Hermitian forms over the ring of integers Rm of an imaginary quadratic field ?(√?m). Using our methods, one can construct expli...Methods are presented for the construction of nondecomposable positive definite integral Hermitian forms over the ring of integers Rm of an imaginary quadratic field ?(√?m). Using our methods, one can construct explicitly an n-ary nondecomposable positive definite Hermitian Rm-lattice ( L, h) with given discriminant 2 for every n?2 (resp. n?13 or odd n?3) and square-free m = 12 k + t with k?1 and t∈ (1,7) (resp. k?1 and t = 2 or k?0 and t∈ 5,10,11). We study also the case for discriminant different from 2.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Methods are presented for the construction of nondecomposable positive definite integral Hermitian forms over the ring of integers Rm of an imaginary quadratic field ?(√?m). Using our methods, one can construct explicitly an n-ary nondecomposable positive definite Hermitian Rm-lattice ( L, h) with given discriminant 2 for every n?2 (resp. n?13 or odd n?3) and square-free m = 12 k + t with k?1 and t∈ (1,7) (resp. k?1 and t = 2 or k?0 and t∈ 5,10,11). We study also the case for discriminant different from 2.
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
