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Ellitpic curves and modular functions

Part of the Lecture Notes in Mathematics book series (LNM,volume 476)

Keywords

  • Modular Form
  • Elliptic Curve
  • Elliptic Curf
  • Abelian Variety
  • Double Point

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. ATKIN A.O.L. and LEHNER J., Hecke operators on Γ0(m). Math. Ann. 185 (1970), 134–160.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. DELIGNE P., Les constantes des équations fonctionnelles. Séminaire Delange-Pisot-Poitou (1969/70), 19 bis.

    Google Scholar 

  3. DELIGNE P. and RAPOPORT M., Les schémas de modules de courbes elliptiques. Modular Functions of One Variable II (Springer Lecture Notes, vol. 349), 143–316.

    Google Scholar 

  4. IGUSA J., Kroneckerian models of fields of elliptic modular functions. Amer. J. Math. 81 (1959), 561–577.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. MAZUR B. and SWINNERTON-DYER H.P.F., Arithmetic of Weil curves. Inventiones Math. 25 (1974), 1–61.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. NÉRON A. Modèles minimaux des variétés abéliennes sur les corps locaux et globaux. Publ. Math. I.H.E.S. 21 (1964), 5–128.

    Google Scholar 

  7. OGG A.P., Elliptic curves and wild ramification. Amer. J. Math. 89 (1967), 1–21.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. SERRE J-P., Abelian ℓ-adic representations and elliptic curves. (New York, 1968).

    Google Scholar 

  9. SHIMURA G., Correspondances modulaires et les fonctions ξ de courbes algébriques. J. Math. Soc. Japan 10 (1958), 1–28.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. SHIMURA G., Introduction to the arithmetic theory of automorphic functions. (Princeton, 1971).

    Google Scholar 

  11. SWINNERTON-DYER H.P.F., Analytic theory of Abelian varieties. (Cambridge, 1974).

    Google Scholar 

  12. WEIL A., Über die Bestimmung Dirichletscher Reihen durch Funktional-gleichungen. Math. Ann. 168 (1967), 149–156.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. MANIN Y.V., Parabolic points and zeta functions of modular forms. (Russian). Izv. Akad. Nauk. (1972), 19–65.

    Google Scholar 

  14. OGG A.P., Modular forms and Dirichlet series. New-York-Amsterdam: Benjamin 1969.

    MATH  Google Scholar 

  15. SERE J-P., Propriétés galoisiennes des points d'ordre fini des courbes elliptiques. Inventiones Math. 15 (1972), 259–331.

    CrossRef  Google Scholar 

  16. SWINNERTON-DYER H.P.F., The conjectures of Birch and Swinnerton-Dyer, and of Tate. Proc. conference on local fields, Driebergen, pp. 132–157. Berlin-Heidelberg-New York: Springer 1967.

    Google Scholar 

  17. TATE J.T., The arithmetic of elliptic curves. Inventiones Math. 23 (1974), 179–206.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. TINGLEY D.J., Computation of elliptic curves parametrised by modular functions. Thesis, Oxford 1975.

    Google Scholar 

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© 1975 Springer-Verlag Berlin · Heidelberg

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Swinnerton-Dyer, H.P.F., Birch, B.J. (1975). Ellitpic curves and modular functions. In: Birch, B.J., Kuyk, W. (eds) Modular Functions of One Variable IV. Lecture Notes in Mathematics, vol 476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097581

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  • DOI: https://doi.org/10.1007/BFb0097581

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07392-5

  • Online ISBN: 978-3-540-37588-3

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