A functional relation for L-functions of graphs equivalent to the Riemann Hypothesis for Dirichlet L-functions

2016/01/18 by Friedli, Fabien · 1 citation
#05C50 (Secondary) #11M26 (Primary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1601.04573

Abstract

In this note we define L-functions of finite graphs and study the particular case of finite cycles in the spirit of a previous paper that studied spectral zeta functions of graphs. The main result is a suggestive equivalence between an asymptotic functional equation for these L-functions and the corresponding case of the Generalized Riemann Hypothesis. We also establish a relation between the positivity of such functions and the existence of real zeros in the critical strip of the classical Dirichlet L-functions with the same character.

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