Arithmetic of alternating forms and quaternion hermitian forms
Arithmetic of alternating forms and quaternion hermitian forms
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交替形式和四元数厄密形式的算术
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发表时间：
1963
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通讯作者：
G. Shimura
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作者：
G. Shimura
由模形式得到的Hecke Dirichlet级数可以看作是附在有理数域Q上的一般线性群GL（2，Q）上的ζ-函数。一般来说，我们可以期望对于定义在$Q$上的相当广泛的一类代数群得到这种ζ-函数。为了实现这一点，有必要发展，摆在首位，理论的基本因子的任何代数群$G$的问题。这实际上是在$G$是半单代数的乘法群的情况下完成的。进一步地，M. Eichler [3].在这两种情况下，有基本定理，由于Eichler $[4，5]$和M。Kneser [6]，可称之为群中的逼近定理
Hecke’s Dirichlet series obtained from modular forms can be regarded as zeta-functions attached to the general linear group $GL(2, Q)$ over the rational number field $Q$ . In general, we may expect to obtain zeta-functions of this kind for a fairly wide class of algebraic groups defined over $Q$ . In order to realize this, it is necessary to develop, in the first place, the theory of elementary divisors for any algebraic group $G$ in question. This is actually done in the case where $G$ is the multiplicative group of a semi-simple algebra. Further, the case of the orthogonal group is investigated in detail by M. Eichler [3]. In both cases, there are fundamental theorems, due to Eichler $[4, 5]$ and M. Kneser [6], which may be called the approximation theorem in the group