Geodesic
Non-Archimedean measures connected with Dirichlet series
Sbornik. Mathematics, Tome 28 (1976) no. 2, pp. 216-228 
M. M. Vishik. Non-Archimedean measures connected with Dirichlet series. Sbornik. Mathematics, Tome 28 (1976) no. 2, pp. 216-228. http://geodesic.mathdoc.fr/item/SM_1976_28_2_a5/
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     author = {M. M. Vishik},
     title = {Non-Archimedean measures connected with {Dirichlet} series},
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     volume = {28},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_28_2_a5/}
}
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In this paper we construct $p$-adic Hecke series which correspond to cusp forms for congruence subgroups. We give a construction of complex-valued measures on the Galois group which are connected with Artin $L$-series. Bibliography: 7 titles.

[1] Y. Amice, J. Velu, “Distributions $p$-adique associées aux séries de Hecke”, Journées arithmetiques, Bordeaux, 1974 | MR

[2] Yu. I. Manin, “Periody parabolicheskikh form i $p$-adicheskie ryady Gekke”, Matem. sb., 92 (134) (1973), 376–401 | MR

[3] Yu. I. Manin, “Znacheniya $p$-adicheskikh ryadov Gekke v tselykh tochkakh kriticheskoi polosy”, Matem. sb., 93 (135) (1974), 621–626 | MR | Zbl

[4] M. M. Vishik, Yu. I. Manin, “$p$-adicheskie ryady Gekke mnimykh kvadratichnykh polei”, Matem. sb., 95 (137) (1974), 357–383 | MR | Zbl

[5] André Weil, “Über die Bestimmung Dirichletcher Reihen durch Funktionalgleichungen”, Math. Ann., 168 (1967), 149–156 ; Matematika, 14:6 (1970) | DOI | MR | MR

[6] V. V. Shokurov, “Modulyarnye simvoly starshego vesa”, Funkts. analiz, 10:1 (1976), 95–96 | MR | Zbl

[7] S. Lang, Algebraic number theory, Addison-Wesley, 1970 | MR