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On the square root of special values of certainL-series

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References

  1. Buhler, J.P., Gross, B.H.: Arithmetic on Elliptic Curves with Complex Multiplication II. Invent. Math.79, 11–29 (1985)

    Google Scholar 

  2. Deuring, M.: Die Klassenkörper der komplexen Multiplikation. (Enzy. der Math. Wiss. Band I, 2. Teil, Heft 10, Teil II) Stuttgart: Teubner 1958

    Google Scholar 

  3. Gross, B.H.: Arithmetic on Elliptic Curves with Complex Multiplication. (Lect. Notes Math., vol. 776) Berlin Heidelberg New York: Springer 1980

    Google Scholar 

  4. Gross, B.H.: Minimal Models for Elliptic Curves with Complex Multiplication. Compos. Math.45, 155–164 (1982)

    Google Scholar 

  5. Goldstein, C., Schappacher, N.: Series d'Eisenstein et fonctions L de courbes elliptiques a multiplication complexe. J. Reine Angew. Math.327, 184–218 (1981)

    Google Scholar 

  6. Hecke, E.: Mathematische Werke. Göttingen: Vandenhoeck and Ruprecht 1959

    Google Scholar 

  7. Kolyvagin, V.A.: Finiteness ofE(Q) and the Tate-Shafarevich group ofE overQ for a subclass of Weil curves. Math. USSR, Izv.32, No 3, 523–541 (1989)

    Google Scholar 

  8. Kronecker, L.: Leopold Kronecker's Werke. Leipzig Berlin: Teubner 1929

    Google Scholar 

  9. Lang, S.: Elliptic Functions. Reading: Addison-Wesley 1973

    Google Scholar 

  10. Manin, Y.I.: Cyclotomic fields and Modular Curves. Russ. Math. Surv.26, No. 6, 7–78 (1971)

    Google Scholar 

  11. Rohrlich, D.: The non-vanishing of certain HeckeL-functions at the center of the critical strip. Duke Math. J.47, No 1, 223–232 (1980)

    Google Scholar 

  12. Rubin, K.: Tate-Shafarevich groups andL-functions of elliptic curves with complex multiplition. Invent. Math.89, 527–560 (1987)

    Google Scholar 

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

    Google Scholar 

  14. Shimura, G.: On the zeta-function of an abelian variety with complex multiplication. Ann. Math.94, 504–533 (1971)

    Google Scholar 

  15. Shimura, G.: On the factors of the Jacobian variety of a modular function field. J. Math. Soc. Japan25, 523–544 (1973)

    Google Scholar 

  16. Shimura, G.: Introduction to the arithmetic theory of automorphic functions. Publ. Math. Soc. Japan11 (1971)

  17. Stark, H.:L-series ats=1 IV. Adv. Math.35, 197–235 (1980)

    Google Scholar 

  18. Waldspurger, J.P.: Correspondance de Shimura. J. Math. Pures Appl.59, 1–132 (1980)

    Google Scholar 

  19. Waldspurger, J.P.: Sur les coefficients de Fourier des formes modulaires de poids demi-entier. J. Math. Pures Appl.60, 375–484 (1981)

    Google Scholar 

  20. Weber, H.: Lehrbuch der Algebra, vol. 3. New York: Chelsea 1961

    Google Scholar 

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Authors and Affiliations

  1. Institute for Advanced Study, 08540, Princeton, NJ, USA

    Fernando Rodriguez Villegas

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  1. Fernando Rodriguez Villegas
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Oblatum 6-XI-1990

Partial support for the writing of this paper was provided by NSF grant DMS-8610730

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Villegas, F.R. On the square root of special values of certainL-series. Invent Math 106, 549–573 (1991). https://doi.org/10.1007/BF01243924

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