论文标题
完成与特定类别均质锥相关的本地Zeta功能
Completion of local zeta functions associated with a certain class of homogeneous cones
论文作者
论文摘要
众所周知，Riemann Zeta函数可以完成到Riemann Xi函数$ξ（s）$的意义上，因为其功能方程的函数方程具有较高的对称形式$ξ（1-s）=ξ（s）$。在上一篇论文（TohokuMath。J.72（2020），349--378）中，我们给出了与均匀锥体和其双锥相关的局部和全局Zeta函数之间功能方程式的明确公式。在本文中，我们考虑完成这些局部Zeta功能的完成，并表明，对于某些类别的同质锥体，相关的本地Zeta功能承认了一种完成形式。
It is well known that the Riemann zeta function can be completed to the Riemann xi function $ξ(s)$ in the sense that its functional equation has a higher symmetric form $ξ(1-s)=ξ(s)$. In the previous paper (Tohoku Math. J. 72 (2020), 349--378), we give an explicit formula of functional equations between local and global zeta functions associated with a homogeneous cone and with its dual cone. In this paper, we consider a completion of these local zeta functions and show that, for a certain class of homogeneous cones, the associated local zeta functions admit a kind of completion forms.
