Vol. 273, No. 1, 2015

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On a prime zeta function of a graph

Takehiro Hasegawa and Seiken Saito

Vol. 273 (2015), No. 1, 123–146
Abstract

In the first half of this paper, we introduce a prime zeta function associated with the Ihara zeta function, and study several properties of this function. In the last half, using results of the first half, we present graph-theoretic analogues to Mertens’ theorems.

Keywords
Ihara zeta functions, primes in graphs, Mertens' theorem
Mathematical Subject Classification 2010
Primary: 11N45
Secondary: 05C30, 05C38, 05C50
Milestones
Received: 3 October 2013
Revised: 29 May 2014
Accepted: 4 June 2014
Published: 6 December 2014
Authors
Takehiro Hasegawa
Shiga University
Otsu
Shiga 520-0862
Japan
Seiken Saito
Waseda University
Shinjuku
Tokyo 169-8050
Japan