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    We complete the cassification of unimodular lattices of gen(I\-3) and gen(I\-3⊥<ε>)(ε=8+37) over Z[7]by adjacent lattices method, and obtain h(I\-3)=3,h(I\-3⊥<ε>)=12, and the representative lattices of each class are given.
    利用邻格方法完成了Z[7]上秩 3的单位格种 gen(Ⅰ3 )及秩 4判别式ε=8+37的正定幺模格种W的分类 ,得到了h(Ⅰ3 ) =3,h(W ) =12及每一类的代表格
    the adjacent lattice methods of Kneser are generalized, some adjacent lattice properties of the positive definite unimodular genera of rank 4n and determinant 1 over Z[/d] are given, and the classification of all the positive unimodular lattices of rank 4 over Z[/3]are obtained.
    推广了Kneser的邻格方法,研究了Z[/d]  上的秩4n判别式1的正定幺模种的邻格性质,完成了Z[/3]上秩4的正定幺模格的分类.
    By comprehensive utilizing adjacent lattice mathods and Siegel mass formula, -we obtain the class number of poaitive even unimodular lattices over Q( ) (d is squarefree positive integer) in V In (n≥ 4) is 2 if and only if Q( ),n=4 and Q( ),n=8.
    本文综合利用邻格方法及Siegel mass公式证明了实二次域Q( )上 内的偶幺模 格类数为2当且仅当Q( ),n=4及Q( ). n=8.
    Using generalized adjacent lattice methods and Siegel mass formula we get the following result: The class number h(In) of unit lattice In(n ≥4) over real quadratic field F is 3 if and only if F=(?)
    用邻格方法及Siegel mass公式证明了实二次代数域(?) (d~(1/2))上单位格种gen(In)(n≥4)的类数h(In)=3当且仅当(?)
    Using the generalized adjacent lattices method, we get the classification of the genera of definite unimodular lattices with rank 4 over Q(6~(1/2)) which are positive definite over one archimedean spot ∞1 and negetive definite over another archimedean spot ∞2.
    利用推广的邻格方法,完成了Q(6~(1/2))上秩4的在一个阿基米德除子上正定,在另一阿基米德除子上负定的所有幺模格种的分类.
    The positive definite unimodular lattices,the adjacent lattice relations and the number of adjacent lattice chains of the positive unimodular lattices over Q(8k+1)~(1/2) are given.
    给出了实二次域Q(8k+1)~(1/2)上的正定幺模格种类及其邻格关系和邻格链个数.
    Using the generalized adjacent lattice method,all the positive unimodular lattices of rank ≤ 4 over Q(17) ~(1/2)are classified,their representative forms are also given.
    利用推广的邻格方法,对Q(17)~(1/2)上的秩≤4的所有正定幺模格进行了分类,给出了代表格.
    In this paper ,the author first generalizes the adjacent lattices method which is used byLiterature[1],[2],and[3]; then he tries the method to classify his newly-found genuses. And a rather integrated result is obtained.
    本文推广了文献[1]、[2]、[3]中的邻格方法,对一类新的定么模格进行了分类,得到了较完整的结果。
    In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus gen( I 4 ) is nine and the class number of even unimodular lattices is three, and also gives the representative lattices of each class.
    本文综合利用邻格方法及Siegelmass公式对Z[(1+ 2 1) /2 ]上秩 4的正定幺模格实现了分类 ,得到了gen(I4 )的类数为 9,偶模格的类数为 3,并且给了代表格
 

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