On graph theory Mertens’ theorems

In this paper, we study graph-theoretic analogues 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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Bibliographische Detailangaben
Veröffentlicht in:	Graphs and combinatorics 2016-09, Vol.32 (5), p.1915-1930
Hauptverfasser:	Hasegawa, Takehiro, Saito, Seiken
Format:	Artikel
Sprache:	eng
Schlagworte:	Combinatorics Engineering Design Mathematics Mathematics and Statistics Original Paper
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	In this paper, we study graph-theoretic analogues 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.
ISSN:	0911-0119 1435-5914
DOI:	10.1007/s00373-016-1710-2