Geodesic
The zeta function of a finite category
Documenta mathematica, Tome 18 (2013), pp. 1243-1274.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 citeLeib. Moreover, it is shown that for a covering of finite categories, $\map{P}E{B}$, 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.
Classification : 18G30, 18D30, 30B10, 30B40
Keywords: zeta function of a finite category, Euler characteristics of categories, coverings of small categories, Dedekind conjecture 
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     author = {Noguchi, Kazunori},
     title = {The zeta function of a finite category},
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Noguchi, Kazunori. The zeta function of a finite category. Documenta mathematica, Tome 18 (2013), pp. 1243-1274. http://geodesic.mathdoc.fr/item/DOCMA_2013__18__a11/