Zeta functions of edge-free quotients of graphs

2020/02/17 by Zakharov, Dmitry · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.07275

Abstract

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→ 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 K₄.

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• Zeta functions of abstract isogeny graphs and modular curves

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