Geodesic
A holomorphic version of the Tate-Iwasawa method for unramified $L$-functions.~I
Sbornik. Mathematics, Tome 205 (2014) no. 10, pp. 1473-1491

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Using the Tate-Iwasawa method the problem of meromorphic continuation and of the existence of a functional equation can be solved for the zeta and $L$-functions of one-dimensional arithmetical schemes. A new version of this method is put forward, which looks at the case of curves over a finite field and of unramified $L$-functions. The proof is based on a reduction of the problem to a Cousin problem on the Riemann sphere which is related to the curve under consideration. Bibliography: 16 titles.
Keywords: zeta function, analytic continuation, sum of residues, Cousin problem.
Mots-clés : Poisson formula 
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     author = {A. N. Parshin},
     title = {A holomorphic version of the {Tate-Iwasawa} method for unramified $L${-functions.~I}},
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A. N. Parshin. A holomorphic version of the Tate-Iwasawa method for unramified $L$-functions.~I. Sbornik. Mathematics, Tome 205 (2014) no. 10, pp. 1473-1491. http://geodesic.mathdoc.fr/item/SM_2014_205_10_a4/