The zeta function of a finite category

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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

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Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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