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On the conjecture of Birch and Swinnerton-Dyer

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References

  1. Artin, E., Tate, J.: Class field theory. New York: Benjamin 1967

    Google Scholar 

  2. Birch, B., Swinnerton-Dyer, P.: Notes on elliptic curves II. J. Reine Angew. Math.218, 79–108 (1965)

    Google Scholar 

  3. Coates, J., Wiles, A.: Kummer's criterion for Hurwitz numbers, to appear in Proceedings of the International Conference on Algebraic Number Theory held in Kyoto, Japan, 1976

  4. Damerell, R.:L-functions of elliptic curves with complex multiplication I. Acta Arith.17, 287–301 (1970)

    Google Scholar 

  5. Deuring, D.: Die Zetafunktionen einer algebraischen Kurve vom Geschlechter Eins, I, II, III, IV. Nachr. Akad. Wiss. Göttingen, 85–94 (1953); 13–42 (1955); 37–76 (1956); 55–80 (1957)

  6. Fröhlich, A.: Formal Groups. Lecture Notes in Math.74. Berlin-Heidelberg-New York: Springer 1968

    Google Scholar 

  7. Hasse, H.: Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper, Teil II, 2nd ed. Würzburg-Wien: Physica 1965

    Google Scholar 

  8. Iwasawa, K.: On some modules in the theory of cyclotomic fields. J. Math. Soc. Japan,16, 42–82 (1964)

    Google Scholar 

  9. Lubin, J.: One parameter formal Lie groups overp-adic integer rings. Ann. of Math.80, 464–484 (1964)

    Google Scholar 

  10. Lubin, J., Tate, J.: Formal complex multiplication in local fields. Ann. Math.81, 380–387 (1965)

    Google Scholar 

  11. Mazur, B.: Rational points of abelian varieties with values in towers of number fields. Inventiones math.18, 183–266 (1972)

    Google Scholar 

  12. Robert, G.: Unités elliptiques. Bull. Soc. Math. France, Mémoire36, 1973

  13. Robert, G.: Nombres de Hurwitz et Unités elliptiques. To appear

  14. Sah, H.: Automorphisms of finite groups. J. Algebra10, 47–68 (1968)

    Google Scholar 

  15. Serre, J.P., Tate, J.: Good reduction of abelian varieties. Ann. Math.88, 492–517 (1968)

    Google Scholar 

  16. Shimura, G.: Introduction to the arithmetic theory of automorphic functions. Pub. Math. Soc. Japan,11, 1971

  17. Tate, J.: Algorithm for determining the type of a singular fiber in an elliptic pencil. In: Modular functions of one variable IV. Lecture Notes in Math.476. Berlin-Heidelberg-New York: Springer 1975

    Google Scholar 

  18. Wiles, A.: Higher explicit reciprocity laws. To appear

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Coates, J., Wiles, A. On the conjecture of Birch and Swinnerton-Dyer. Invent Math 39, 223–251 (1977). https://doi.org/10.1007/BF01402975

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  • DOI: https://doi.org/10.1007/BF01402975

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