The zeta function of a finite category
Kazunori Noguchi
Faculty of Science Shinshu University Matsumoto 390-8621 Japan
![The zeta function of a finite category cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-dm-volume-18.png&w=3840&q=90)
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, , 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. 1243–1274
DOI 10.4171/DM/427