The zeta function of a finite category
Kazunori NoguchiFaculty of Science Shinshu University Matsumoto 390-8621 Japan
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, , the zeta function of is that of 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.
Cite this article
Kazunori Noguchi, The zeta function of a finite category. Doc. Math. 18 (2013), pp. 1243–1274DOI 10.4171/DM/427