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Counting and zeta functions over $${\mathbb F}_1$$ F 1:

Deitmar, Anton ; Koyama, Shin-ya ; Kurokawa, Nobushige
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg.  85 (2015)  1 - p. 59-71 , 2015
Link: https://doi.org/10.1007/s12188-015-0104-3