On Certain Zeta Functions Attached to Two Hilbert Modular Forms: I. The Case of Hecke Characters
On Certain Zeta Functions Attached to Two Hilbert Modular Forms: I. The Case of Hecke Characters
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关于附加到两个希尔伯特模形式的某些 Zeta 函数：I. Hecke 字符的情况
DOI：
10.2307/1971381
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发表时间：
1981
影响因子：
4.9
通讯作者：
G. Shimura
中科院分区：
文献类型：
--
作者：
G. Shimura
为了使我们的论述顺利进行，让我们首先介绍一些记号惯例。对于有限次代数数域K，我们用JK表示K到C的所有嵌入的集合，用IK表示由JK的元素生成的自由Z-模。然后我们设置Rik=IK0 R和CIK=IK0 C。如果p=EaPaU E IK，带有E JK和PO E Z。我们设置XP=f1，(Xa)P for 0/x E K；如果xa都是实数和正数，这对p e CIK是有意义的。在整篇文章中，我们用D表示复上半平面，用F表示n次全实代数数域。现在，本文要研究的Zeta函数，当适当地特化时，具有如下形式
To make our exposition smooth, let us first introduce some notational conventions. For an algebraic number field K of finite degree, we denote by JK the set of all embeddings of K into C, and by IK the free Z-module generated by the elements of JK. We then put RIK = IK0 R and CIK = IK0 C. If p = EaPaU E IK with a E JK and PO E Z. we put xP = fl,(xa)Pfor 0 / x E K; this is meaningful for p e CIK if xa are all real and positive. Throughout the paper, we denote by D the complex upper half plane and by F a totally real algebraic number field of degree n. Now the zeta function to be studied in this paper, when suitably specialized, has the form