|
|||||
|
|
|
|
|
|
|
|
|
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 |
|
|
