Geodesic
The zeta function of a finite category
Documenta mathematica, Tome 18 (2013), pp. 1243-1274
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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.
DOI : 10.4171/dm/427
Classification : 18D30, 30B10, 30B40
Mots-clés : zeta function of a finite category, Euler characteristics of categories, coverings of small categories, Dedekind conjecture 
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     author = {Kazunori Noguchi},
     title = {The zeta function of a finite category},
     journal = {Documenta mathematica},
     pages = {1243--1274},
     year = {2013},
     volume = {18},
     doi = {10.4171/dm/427},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/427/}
}
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Kazunori Noguchi. The zeta function of a finite category. Documenta mathematica, Tome 18 (2013), pp. 1243-1274. doi: 10.4171/dm/427

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