Zeta functions for infinite graphs and functional equations
Daniele Guido, Tommaso Isola
TL;DR
This paper reviews the properties of Ihara and Bartholdi zeta functions for infinite graphs, discusses the conditions for their functional equations, and explores potential solutions to these mathematical challenges.
Contribution
It provides a comprehensive review of zeta functions for infinite graphs and investigates the conditions under which their functional equations hold.
Findings
Analysis of the properties of Ihara and Bartholdi zeta functions
Discussion of the validity of functional equations for these zeta functions
Proposals for possible solutions to functional equation issues
Abstract
The definitions and main properties of the Ihara and Bartholdi zeta functions for infinite graphs are reviewed. The general question of the validity of a functional equation is discussed, and various possible solutions are proposed.
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