Geodesic
$\zeta$-functions of some one-dimensional rings
Izvestiya. Mathematics , Tome 7 (1973) no. 1, pp. 1-17.

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The notion of the zeta-function is generalized to rings which are orders in classical Dedekind rings; the structure of these functions is explained. Classes of rings are given for which the classical assertions (the Riemann hypothesis, functional equation) are applicable. 
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V. M. Galkin. $\zeta$-functions of some one-dimensional rings. Izvestiya. Mathematics , Tome 7 (1973) no. 1, pp. 1-17. http://geodesic.mathdoc.fr/item/IM2_1973_7_1_a0/

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