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
For any natural numbers m and n≥17 we can construct explicitly indecomposable definite unimodular normal Hermitian lattices of rank n over the ring of algebraic integers R<sub>m</sub> in an imaginary quad...For any natural numbers m and n≥17 we can construct explicitly indecomposable definite unimodular normal Hermitian lattices of rank n over the ring of algebraic integers R<sub>m</sub> in an imaginary quadratic field (-m<sup>1/2</sup>). It is proved that for any n （in case m=11, there is one exception n=3） there exist indecomposable definite unimodular normal Hermitian R<sub>15</sub>(R<sub>11</sub>- lattices of rank n, and we exhibit representatives for each class. In the exceptional case there are no lattices with the desired properties. The method given in this paper can solve completely the problem of constructing indecomposable definite unimodular normal Hermitian R<sub>m</sub>-lattices of any rank n for each m.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For any natural numbers m and n≥17 we can construct explicitly indecomposable definite unimodular normal Hermitian lattices of rank n over the ring of algebraic integers R<sub>m</sub> in an imaginary quadratic field (-m<sup>1/2</sup>). It is proved that for any n （in case m=11, there is one exception n=3） there exist indecomposable definite unimodular normal Hermitian R<sub>15</sub>(R<sub>11</sub>- lattices of rank n, and we exhibit representatives for each class. In the exceptional case there are no lattices with the desired properties. The method given in this paper can solve completely the problem of constructing indecomposable definite unimodular normal Hermitian R<sub>m</sub>-lattices of any rank n for each m.
