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A generalization of a graph theory Mertens’ theorem: Galois covering case

Takehiro Hasegawa , Seiken Saito EMAIL logo and Iwao Sato
From the journal Forum Mathematicum

Abstract

In 1874, Franz Mertens proved the so-called Mertens’ theorem, and in 1974, Kenneth S. Williams showed Mertens’ theorem associated with a character. In a previous paper, we presented a graph-theoretic analogue to Williams’ theorem. In this paper, we generalize our previous work in the sense that a character is extended to a representation. To our knowledge, a number-theoretic analogue to our result is not yet known. So, we expect that, by using our methods, it can be proven in the future.


Communicated by Jörg Brüdern


Award Identifier / Grant number: 15K17508

Award Identifier / Grant number: 16K05259

Award Identifier / Grant number: 15K04985

Funding statement: Takehiro Hasegawa was partially supported by JSPS KAKENHI (grant number 15K17508). Seiken Saito was partially supported by JSPS KAKENHI (grant number 16K05259). Seiken Saito acknowledges that part of this work was carried out under a Waseda University Grant for Special Research Projects (project number 2015B-498 and 2017K-383). Iwao Sato was partially supported by JSPS KAKENHI (grant number 15K04985).

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Received: 2016-3-2
Published Online: 2017-8-17
Published in Print: 2018-5-1

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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