论文标题
图形的无边缘商的Zeta功能
Zeta functions of edge-free quotients of graphs
论文作者
论文摘要
我们考虑ihara zeta函数$ζ（u，x // g）$和artin-ihara $ l $ l $ - grupt $ x // g $的商图的功能，其中$ g $是在有限图$ x $上具有琐碎边缘稳定器的$ x $。我们确定了$ x $和$ x // g $的素数之间的关系，并表明$ x \ to x // g $自然可以看作是群体图形的未受到的galois覆盖。我们表明，以常规表示情况评估的$ x // g $的$ l $ function等于$ζ（u，x）$，$ζ（u，x // g）$ divides $ζ（u，x）$。我们为Zeta和$ l $ functions得出了两项和三项决定因素公式，并计算了几个$ l $ functions的$ l $ functions tetrahedron Graph $ k_4 $的示例。
We consider the Ihara zeta function $ζ(u,X//G)$ and Artin-Ihara $L$-function of the quotient graph of groups $X//G$, where $G$ is a group acting on a finite graph $X$ with trivial edge stabilizers. We determine the relationship between the primes of $X$ and $X//G$ and show that $X\to X//G$ can be naturally viewed as an unramified Galois covering of graphs of groups. We show that the $L$-function of $X//G$ evaluated at the regular representation is equal to $ζ(u,X)$ and that $ζ(u,X//G)$ divides $ζ(u,X)$. We derive two-term and three-term determinant formulas for the zeta and $L$-functions, and compute several examples of $L$-functions of edge-free quotients of the tetrahedron graph $K_4$.
