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Local units, elliptic units, Heegner points and elliptic curves

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References

  1. Atiyah, M., Wall, C.: Cohomology of groups. In: Algebraic number theory. Cassels J.W.S., Fröhlich, A. (eds.), pp. 94–115, London: Academic Press 1967

    Google Scholar 

  2. Birch, B., Stephens, N.: Computation of Heegner points. In: Modular forms. Rankin, R.A. (ed.), pp. 13–41, Chichester: Ellis Horwood Ltd (1984)

    Google Scholar 

  3. Coates, J.: Elliptic curves and Iwasawa theory. In: Modular forms. Rankin, R.A. (ed.), pp. 51–73. Chichester: Ellis Horwood Ltd (1984)

    Google Scholar 

  4. Coates, J., Wiles, A.: On the conjecture of Birch and Swinnerton-Dyer. Invent. Math.39, 223–251 (1977)

    Google Scholar 

  5. Coates, J., Wiles, A.: Onp-adicL-functions and elliptic units. J. Austr. Math. Soc.26, 1–25 (1978)

    Google Scholar 

  6. Coleman, R.: Division values in local fields. Invent. Math.53, 91–116 (1979)

    Google Scholar 

  7. Greenberg, R.: On the Birch and Swinnerton-Dyer conjecture. Invent. Math.72, 241–265 (1983)

    Google Scholar 

  8. Greenberg, R.: On the structure of certain Galois groups. Invent. Math.47, 85–99 (1978)

    Google Scholar 

  9. Gross, B.: Arithmetic on elliptic curves with complex multiplication Lect. Notes Math. vol.776. Berlin-Heidelberg-New York: Springer 1980

    Google Scholar 

  10. Gross, B.: Heegner points onX o(N). In: Modular forms. Rankin, R.A. (ed.), pp. 87–105. Chichester: Ellis Horwood Ltd (1984)

    Google Scholar 

  11. Gross, B., Zagier, D.: Points de Heegner et dérivées de fonctions L. C.R. Acad. Sci. Paris297, 85–87 (1983)

    Google Scholar 

  12. Hazewinkel, M.: On norm maps for one-dimensional formal groups III. Duke Math. J.44, 305–314 (1977)

    Google Scholar 

  13. Montgomery, H., Rohrlich, D.: On theL-functions of canonical Hecke characters of imaginary quadratic fields II. Duke Math. J.49, 937–942 (1982)

    Google Scholar 

  14. Rohrlich, D.: OnL-functions of elliptic curves and anticyclotomic towers. Invent. Math.75, 383–408 (1984)

    Google Scholar 

  15. Rubin, K.: Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer. Invent. Math.64, 455–470 (1981)

    Google Scholar 

  16. Rubin, K.: Elliptic curves andZ p -extensions. Compos. Math.56, 237–250 (1985)

    Google Scholar 

  17. Shimura, G.: On elliptic curves with complex multiplication as factors of the jacobians of modular function fields. Nagoya Math. J.43, 199–208 (1971)

    Google Scholar 

  18. Shimura, G.: Introduction to the arithmetic theory of automorphic forms. Princeton: Princeton Univ. Press 1971

    Google Scholar 

  19. Tate, J.: WC-groups overp-adic fields. Séminaire Bourbaki (1957/1958) exposé 156

  20. Waldspurger, J-L.: Sur les valeurs de certaines fonctionsL automorphes en leur centre de symétrie. Compos. Math.54, 173–242 (1985)

    Google Scholar 

  21. Wiles, A.: Higher explicit reciprocity laws. Ann. Math.107, 235–254 (1978)

    Google Scholar 

  22. Wintenberger, J-P.: Structure galoisienne de limites projectives d'unités locales. Compos. Math.42, 89–103 (1981)

    Google Scholar 

  23. Yager, R.: On two variablep-adicL-functions. Ann. Math.115, 411–449 (1982)

    Google Scholar 

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Partially supported by NSF grant DMS-8501937

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Rubin, K. Local units, elliptic units, Heegner points and elliptic curves. Invent Math 88, 405–422 (1987). https://doi.org/10.1007/BF01388915

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