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On graph theory Mertens’ theorems

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Abstract

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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Acknowledgments

The authors thank the referee for his or her valuable comments and careful review of this paper.

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Authors and Affiliations

  1. Shiga University, Otsu, Shiga, 520-0862, Japan

    Takehiro Hasegawa

  2. Waseda University, Shinjuku, Tokyo, 169-8050, Japan

    Seiken Saito

Authors
  1. Takehiro Hasegawa
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  2. Seiken Saito
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Corresponding author

Correspondence to Seiken Saito.

Additional information

Takehiro Hasegawa was partially supported by JSPS KAKENHI Grant Number 15K17508.

Seiken Saito was partially supported by JSPS KAKENHI Grant Number 16K05259.

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Hasegawa, T., Saito, S. On graph theory Mertens’ theorems. Graphs and Combinatorics 32, 1915–1930 (2016). https://doi.org/10.1007/s00373-016-1710-2

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  • DOI: https://doi.org/10.1007/s00373-016-1710-2

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