四元代数上图的顶点加权 Zeta 函数

doi:10.12677/PM.2023.134081

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四元代数上图的顶点加权 Zeta 函数
Vertex-Weighted Zeta Function of the Quaternion Algebraic Graph

DOI: 10.12677/PM.2023.134081, PDF, HTML, 下载: 308 浏览: 440
作者: 李淑雅：上海理工大学理学院，上海
关键词: Ihara Zeta 函数；Study 行列式；顶点加权；Ihara Zeta Function； Study Determinant； Vertex Weighting

摘要: 给定一个有向图，建立了一个图上的四元数顶点加权 zeta 函数及其 Study 行列式表达式。对于顶点上有四元数权值的图，我们通过使用无限积来定义 zeta 函数，将其视为欧拉积。这是 Ihara zeta 函数在四元数上的扩展。给出新的 zeta 函数的两个 Study 行列式表达式。

Abstract: Given a directed graph, a quaternion vertex weighted zeta function on the graph and its Study determinant expression are established. For graphs with quaternion weights on vertices, we deﬁne zeta functions by using inﬁnite products as Euler products. This is an extension of the Ihara zeta function on quaternions. Two Study determinant expressions of the new zeta function are given.

文章引用：李淑雅. 四元代数上图的顶点加权 Zeta 函数[J]. 理论数学, 2023, 13(4): 781-794. https://doi.org/10.12677/PM.2023.134081

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