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

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• 作者：Fabien Friedli¹ ; ^{fabien.friedli@unige.ch" class="auth_mail" title="E-mail the corresponding author}
• 关键词：L-functions of graphs ; Dirichlet L-functions ; Functional equations ; Generalized Riemann Hypothesis ; Cyclic graphs
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：169
• 期：Complete
• 页码：342-352
• 全文大小：289 K

文摘

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.