Geodesic
The zeta-function of elliptic curves over certain Abelian extensions of imaginary quadratic fields
Sbornik. Mathematics, Tome 31 (1977) no. 1, pp. 49-62 Cet article a éte moissonné depuis la source Math-Net.Ru

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For certain elliptic curves defined over an imaginary quadratic field, the value at one of the canonical $L$-series of these curves with explicit Dirichlet characters of the ground field is proved to equal zero. Bibliography: 9 titles. 
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P. F. Kurchanov. The zeta-function of elliptic curves over certain Abelian extensions of imaginary quadratic fields. Sbornik. Mathematics, Tome 31 (1977) no. 1, pp. 49-62. http://geodesic.mathdoc.fr/item/SM_1977_31_1_a3/

[1] A. Atkin, J. Lehner, “Hecke operators on $\Gamma_0(m)$”, Math. Ann., 185:2 (1970), 134–160 | DOI | MR | Zbl

[2] H. Jacquet, Automorphic forms on $GL(2)$, part II, Lecture Notes in Math., 278, Springer-Verlag, Berlin, 1972 | MR | Zbl

[3] T. Miyake, “On automorphic forms on $GL_2$ and Hecke operators”, Ann. Math., 94 (1971), 174–189 | DOI | MR

[4] A. Weil, Dirichlet series and automorphic formes, Lecture Notes in Math., 189, Springer-Verlag, Berlin, 1971 | Zbl

[5] R. Godeman, “Zametki po teorii Zhake-Lenglendsa”, Matematika, 18:2 (1974), 28–78

[6] E. Zhake, R. Lenglends, Avtomorfnye formy na $GL(2)$, izd-vo «Mir», Moskva, 1973 | MR

[7] P. F. Kurchanov, “Ellipticheskie krivye beskonechnogo ranga nad $\Gamma$-rasshireniyami”, Matem. sb., 90 (132) (1973), 320–324 | Zbl

[8] S. Leng, Algebraicheskie chisla, izd-vo «Mir», Moskva, 1966 | MR

[9] Yu. I. Manin, “Parabolicheskie tochki i dzeta-funktsii modulyarnykh krivykh”, Izv. AN SSSR, seriya matem., 36 (1972), 19–66 | MR | Zbl