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

作者：Friedli Fabien^*

来源：Journal of Number Theory, 2016, 169: 342-352.

DOI：10.1016/j.jnt.2016.05.025

• L-functions of graphs
• Dirichlet L-functions
• Functional equations
• Generalized Riemann Hypothesis
• Cyclic graphs

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.

• 出版日期2016-12