Q((-43)^(1/2))上的正定厄米特型的分类(英文)

Classification of Positive Definite Hermitian Forms over Q(■)

设D为Q（■）上的整数环，Cn,△n为D上判别式为△n的n元正定厄米特型的类数，本文应用厄米简化理论，给出了m＝2，1≤△n≤5和n＝3，△n＝1的厄米特型的类数，同时也给出了各类的代表型。

Let D be the ring of integers in the imaginary quadratic field Q() and let Cn,△n be the class number of a positive de finits Hermitian form of rank n and discriminant △n over D. In this paper the author determines Cn ,△n with n = 2, 1≤△n≤5 and n = 3, △n= 1 by usin Hermitian reduction theory to Hermitian forms over D. Representative forms of classes are exhibited.