On graph theory Mertens' theorems
Takehiro Hasegawa, Seiken Saito
TL;DR
This paper explores graph-theoretic analogies of Mertens' theorems using Ihara zeta-functions, refining a specific case of the dynamical system Mertens' second theorem.
Contribution
It introduces a novel graph-theoretic perspective on Mertens' theorems and refines existing results in the context of dynamical systems.
Findings
Refined a special case of Mertens' second theorem for dynamical systems.
Established graph-theoretic analogies using Ihara zeta-functions.
Enhanced understanding of the connection between graph theory and number theory.
Abstract
In this paper, we study graph-theoretic analogies of the Mertens' theorems by using basic properties of the Ihara zeta-function. One of our results is a refinement of a special case of the dynamical system Mertens' second theorem due to Sharp and Pollicott.
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Taxonomy
TopicsGraph theory and applications · Computational Drug Discovery Methods