A new generalized Bartholdi zeta function for a digraph

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.

Keywords:

• Zeta function
• digraph covering
• L-function

2000 Mathematical Subject Classifications:

• 05C50
• 15A15

Acknowledgements

We would like to thank the referee for many useful suggestions and comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author is partially supported by the Grant-in-Aid for Scientific Research (C) of Japan Society for the Promotion of Science (Grant No. 16K05249). The second author is partially supported by the Grant-in-Aid for Young Scientists (B) of Japan Society for the Promotion of Science (Grant No. 26400001). The third author is partially supported by the Grant-in-Aid for Scientific Research (C) of Japan Society for the Promotion of Science (Grant No. 15K04985).