论文标题
关于Hecke L功能的算术的注释
Notes on the arithmetic of Hecke L-functions
论文作者
论文摘要
这是一篇说明性文章，涉及代数IDELE类字符的各种相关概念，Hecke的Groessencharaktere以及GL（1）的同胞自动形式表示，均为代数Hecke字符的一般标题。本文的第一部分系统地奠定了代数Hecke字符的基础。唯一的先决条件是：基本代数数理论，对Adelic语言的熟悉以及基本的捆式理论。还讨论了在自动形态L功能算术中起着至关重要的作用的观察结果。本文的第二部分，就代数Hecke角色附加的Hecke L功能的连续临界值的比率与Guenter定理的某些变化更加困难，尤其是引起人们对微妙的签名的关注，而这些签名显然没有注意到。
This is an expository article that concerns the various related notions of algebraic idele class characters, the Groessencharaktere of Hecke, and cohomological automorphic representations of GL(1), all under the general title of algebraic Hecke characters. The first part of the article systematically lays the foundations of algebraic Hecke characters. The only pre-requisites are: basic algebraic number theory, familiarity with the adelic language, and basic sheaf theory. Observations that play a crucial role in the arithmetic of automorphic L-functions are also discussed. The second part of the article, on the ratios of successive critical values of the Hecke L-function attached to an algebraic Hecke character, concerns certain variations on a theorem of Guenter Harder, especially drawing attention to a delicate signature that apparently has not been noticed before.
