A new generalized Bartholdi zeta function for a digraph. Issue 6 (26th April 2021)

• Record Type: Journal Article
• Authors: Mitsuhashi, Hideo; Morita, Hideaki; Sato, Iwao
• Is Part Of: Linear & multilinear algebra. Volume 69:Issue 6(2021)
• Page Start: 1045
• Page End: 1060
• Publication Date: 2021-04-26
• Subjects: Zeta function -- digraph covering -- L-function; 05C50 -- 15A15; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2019.1620165
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : We define a new generalized Bartholdi zeta function of a digraph D, and give a determinant expression of it. We present a decomposition formula for the new generalized Bartholdi zeta function of a group covering of D . Furthermore, we introduce a new generalized Bartholdi L -function of D, and give a determinant expressions of it. As an application, we present a decomposition formula for the new generalized Bartholdi zeta function of a group covering of D by its new generalized Bartholdi L -functions.