References
Arthaud, N.: On Birch and Swinnerton-Dyer's conjecture for elliptic curves with complex multiplication. I. Comp. Math.37, 209–232 (1978)
Brumer, A.: On the units of algebraic number fields. Mathematika14, 121–124 (1967)
Coates, J.: Infinite descent on elliptic curves with complex multiplication. To appear in Progress in Mathematics. Boston: Birkhauser
Coates, J.: Elliptic curves with complex multiplication. Herman Weyl lectures, 1979, Annals of Math. Studies, to appear
Coates, J., Wiles, A.: On the conjecture of Birch and Swinnerton-Dyer. Invent. Math.39, 223–251 (1977)
Damarell, R.:L-functions of elliptic curves with complex multiplication I. Acta Arith.17, 287–301 (1970)
Deuring, M.: Die Zetafunktionen einer algebraischen Kurve vom Geschlecht Eins I, II, III, IV. Nachr. Akad. Wiss. Göttingen, 85–94 (1953); 13–42 (1955); 37–76 (1956); 53–80 (1957)
Frohlich, A., Queyrut, J.: On the functional equation of the ArtinL-function for characters of real representations. Invent. Math.14, 173–183 (1971)
Greenberg, R.: Onp-adicL-functions and Iwasawa's theory for imaginary quadratic fields Proceedings of conference on modern trends in Alg. No. theory related to Fermat's last theorem, pp. 215–286. Boston: Birkhäuser
Greenberg, R.: Functional equations, root numbers, and Iwasawa theory. In preparation
Gross, B., Zagier, D.: On the critical values of HeckeL-series. Soc. Math. de France, Memoire No.2, 49–54 (1980)
Hardy, G.H.: Divergent Series. Clarendon Press (1949)
Iwasawa, K.: On ℤ t -extension of algebraic number fields. Ann. of Math.98, 246–326 (1973)
Katz, N.:p-adic interpolation of real analytic Eisenstein series. Ann. of Math.104, 459–571 (1976)
Kohnen, W., Zagier, D.: Values ofL-series of modular forms at the center of the critical strip. Invent. Math.64, 175–198 (1981)
Manin, J., Vishik, S.:p-adic Hecke series for imaginary quadratic fields. Math. Sbornik95 (137) (1974), No. 3
Martinet, J.: Character theory and ArtinL-functions. Alg. No. fields. (Frohlich, A. (ed.) New York: Academic Press (1977)
Mazur, B.: Rational points of abelian varieties with values in towers of number fields. Invent. Math.18, 183–266 (1972)
Ogg, A.: Modular forms and dirichlet series. New York: Benjamin 1969
Perrin-Riou, B.: Groupe de Selmer d'une courbe elliptique a multiplication complexe. Comp. Math.43, 387–417 (1981)
Rubin, K.: Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer. Invent. Math.64, 455–470 (1981)
Rubin, K., Wiles, A.: Mordell-Weil groups of elliptic curves over cyclotomic fields. Proceedings of conference on modern trends in Alg. No. theory related to Fermat's last theorem, pp. 237–254. Boston: Birkhäuser
Serre, JP.: Classes de corps cyclotomique. Sem. Bourbaki174 (1958)
Serre, JP, Tate, J.: Good reduction of abelian varieties. Ann. Math.88, 492–517 (1968)
Shimura, G.: On elliptic curves with complex multiplication as factors of the Jacobian of modular function fields. Nagoya Math. J.43, 199–208 (1971)
Tate, J.: Fourier analysis in number fields and Hecke's zeta functions. Alg. No. theory. (Cassels, Frohlich, eds.). London: Academic Press 305–347 (1967)
Tate, J.: Arithmetic of elliptic curves. Invent. Math.23, 179–206 (1974)
Tate, J. Local constants. Alg. No. fields, (Frohlich, A., ed.). New York: Academic Press 1977
Weil, A.: On a certain type of character of the idele-class groups of an algebraic number field. Proc. Int'l. Symp. Tokyo-Nikko, 1–7 1955
Weil, A.: Dirichlet series and automorphic forms. Lecture notes in math. Vol. 189. Berlin-Heidelberg-New York: Springer 1971
Yager, R.: On two-variablep-adicL-functions. Ann. of Math.115, 411–449 (1982)
Yager, R.:p-adic measures on Galois groups. Preprint
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Greenberg, R. On the Birch and Swinnerton-Dyer conjecture. Invent Math 72, 241–265 (1983). https://doi.org/10.1007/BF01389322
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DOI: https://doi.org/10.1007/BF01389322