Q((-11)^(1/2))上正定Hermite型的分类(英文)

CLASSIFICATION OF POSITIVE DEFINITE HERMITIAN FORMS OVER Q((-11)^(1/2))

设 R 为虚二次域 Q(-11)^(1/2)的代数整数环,C_(n,Δ_n) 为秩 n 而判别式=Δ_n 的 R上正定 Hermite 型的类数。作者应用 Hermite 约简理论确定了类数 C_(2,3)=C_(2,4)=C_(2,5)=2;C_(3,2)=C_(3,3)=3;C_(4,1)=5并给出了每一类的代表型。

Let R be the risg of integers in the imaginary quadratic fieldQ((-11)^(1/2)) and let C_(n,Δn) be the class number of positive definite Hermitianform of rank n and discriminant Δ_n over R.In this paper the author determi-nes C_(n,Δ_n),by using Hermitian reduction theory to Hermitian forms over R,namely C_(2,3)=C_(2,4)=C_(2,5)=2;C_(3,2)=C_(3,3)=3;C_(4,1)=5.Representative forms ofeach class are exhibited.