论文标题
Riemann运营商在Quillen的高$ K $ -Groups上的决定因素：周期性
Determinants of Riemann operators on Quillen's higher $K$-groups: periodicity
论文作者
论文摘要
在上一篇论文[KT]中，我们在Quillen的较高$ k $ -groups the代数数字字段$ k $的整数环上介绍了Riemann运营商的决定因素。我们表明，决定因素实际上表达了$ k $的Dedekind Zeta函数所谓的伽马因子的倒数。 在这里，我们研究了决定因素的周期性。这来自著名的$ k $组的著名“周期性”。该周期性类似于Euler的伽马功能$γ（x+1）=xγ（x）$的周期性。我们还研究了与Euler的反射公式$γ（x）γ（1-x）= \fracπ{\ sin（πx）} $相对应的“反射公式”。
In a previous paper [KT] we introduced determinant of the Riemann operator on Quillen's higher $K$-groups of the integer ring of an algebraic number field $K$. We showed that the determinant expresses essentially the inverse of the so called gamma factor of Dedekind zeta function of $K$. Here we study the periodicity of determinant. This comes from the famous "periodicity" of higher $K$ groups. This periodicity is analogous to Euler's periodicity of gamma function $Γ(x+1)=xΓ(x)$. We investigate the "reflection formula" corresponding to Euler's reflection formula $Γ(x)Γ(1-x)=\fracπ{\sin(πx)}$ also.
