论文标题
全局字段量表
Global Field Totients
论文作者
论文摘要
使用其余定理来估价一个字段，我们就全球字段的规范功能提供了新的观点。我们定义了全局字段的Euler成立函数，并恢复经典算术函数的基本分析特性，即产品公式。此外，我们证明了相关的Zeta函数的全态性。作为应用程序，我们通过Weiner-ikehara定理恢复了Erdős，Dressler和Bateman的平均值定理的类似物。
Using a remainder theorem for valuations of a field, we give a new perspective on the norm function of a global field. We define the Euler totient function of a global field and recover the essential analytical properties of the classical arithmetical function, namely the product formula. In addition, we prove the holomorphicity of the associated zeta function. As an application, we recover the analog of the mean value theorem of Erdős, Dressler, and Bateman via the Weiner-Ikehara theorem.
