The zeta function of a finite category

Kazunori Noguchi

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We define the zeta function of a finite category. We prove a theorem that states a relationship between the zeta function of a finite category and the Euler characteristic of finite categories, called the series Euler characteristic [BL08]. Moreover, it is shown that for a covering of finite categories, P: E → B, the zeta function of E is that of B to the power of the number of sheets in the covering. This is a categorical analogue of the unproved conjecture of Dedekind for algebraic number fields and the Dedekind zeta functions.

Original languageEnglish
Pages (from-to)1243-1274
Number of pages32
JournalDocumenta Mathematica
Volume18
Issue number2013
Publication statusPublished - 2013 Jan 1
Externally publishedYes

Fingerprint

Riemann zeta function
Euler Characteristic
Covering
Unproved
Dedekind zeta Function
Algebraic number Field
Categorical
Analogue
Series
Theorem

Keywords

  • Coverings of small categories
  • Dedekind conjecture
  • Euler characteristics of categories
  • Zeta function of a finite category

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Noguchi, K. (2013). The zeta function of a finite category. Documenta Mathematica, 18(2013), 1243-1274.

The zeta function of a finite category. / Noguchi, Kazunori.

In: Documenta Mathematica, Vol. 18, No. 2013, 01.01.2013, p. 1243-1274.

Research output: Contribution to journalArticle

Noguchi, K 2013, 'The zeta function of a finite category', Documenta Mathematica, vol. 18, no. 2013, pp. 1243-1274.
Noguchi K. The zeta function of a finite category. Documenta Mathematica. 2013 Jan 1;18(2013):1243-1274.
Noguchi, Kazunori. / The zeta function of a finite category. In: Documenta Mathematica. 2013 ; Vol. 18, No. 2013. pp. 1243-1274.
@article{a5a6d93c79754b07a83acf35c78c2c74,
title = "The zeta function of a finite category",
abstract = "We define the zeta function of a finite category. We prove a theorem that states a relationship between the zeta function of a finite category and the Euler characteristic of finite categories, called the series Euler characteristic [BL08]. Moreover, it is shown that for a covering of finite categories, P: E → B, the zeta function of E is that of B to the power of the number of sheets in the covering. This is a categorical analogue of the unproved conjecture of Dedekind for algebraic number fields and the Dedekind zeta functions.",
keywords = "Coverings of small categories, Dedekind conjecture, Euler characteristics of categories, Zeta function of a finite category",
author = "Kazunori Noguchi",
year = "2013",
month = "1",
day = "1",
language = "English",
volume = "18",
pages = "1243--1274",
journal = "Documenta Mathematica",
issn = "1431-0635",
publisher = "Deutsche Mathematiker Vereinigung",
number = "2013",

}

TY - JOUR

T1 - The zeta function of a finite category

AU - Noguchi, Kazunori

PY - 2013/1/1

Y1 - 2013/1/1

N2 - We define the zeta function of a finite category. We prove a theorem that states a relationship between the zeta function of a finite category and the Euler characteristic of finite categories, called the series Euler characteristic [BL08]. Moreover, it is shown that for a covering of finite categories, P: E → B, the zeta function of E is that of B to the power of the number of sheets in the covering. This is a categorical analogue of the unproved conjecture of Dedekind for algebraic number fields and the Dedekind zeta functions.

AB - We define the zeta function of a finite category. We prove a theorem that states a relationship between the zeta function of a finite category and the Euler characteristic of finite categories, called the series Euler characteristic [BL08]. Moreover, it is shown that for a covering of finite categories, P: E → B, the zeta function of E is that of B to the power of the number of sheets in the covering. This is a categorical analogue of the unproved conjecture of Dedekind for algebraic number fields and the Dedekind zeta functions.

KW - Coverings of small categories

KW - Dedekind conjecture

KW - Euler characteristics of categories

KW - Zeta function of a finite category

UR - http://www.scopus.com/inward/record.url?scp=84918806386&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84918806386&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84918806386

VL - 18

SP - 1243

EP - 1274

JO - Documenta Mathematica

JF - Documenta Mathematica

SN - 1431-0635

IS - 2013

ER -