Geodesic
Sur les formules explicites de th\'eorie des nombres
Izvestiya. Mathematics , Tome 6 (1972) no. 1, pp. 1-17

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"Explicit formulas" in number theory express the sum of values of a function at the zeros of an $L$-series of an algebraic number field as a sum of local terms corresponding to all norms of this field. For the case of Hecke $L$-series, such formulas were found earlier by the author. In this paper they are derived for Artin–Hecke series corresponding to arbitrary finite-dimensional representations of the group $W_{k,K}$ – the standard extension of the idele class group of a global field $K$ using the Galois group of a finite extension $K/k$. In this connection it turns out that terms corresponding to archimedean and nonarchimedean norms can be written in unique form. 
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A. Weil. Sur les formules explicites de th\'eorie des nombres. Izvestiya. Mathematics , Tome 6 (1972) no. 1, pp. 1-17. http://geodesic.mathdoc.fr/item/IM2_1972_6_1_a0/