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

JOURNAL OF NUMBER THEORY

卷:169

Article

Friedli, Fabien¹ 

[1] Univ Geneva, Sect Math, 2-4 Rue Lievre,Case Postale 64, CH-1211 Geneva 4, Switzerland

关键词: L-functions of graphs;    Dirichlet L-functions;    Functional equations;    Generalized Riemann Hypothesis;    Cyclic graphs;   

DOI  :  10.1016/j.jnt.2016.05.025

来源: Elsevier

【 摘 要 】

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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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