Inventiones mathematicae

, Volume 25, Issue 1, pp 1–61 | Cite as

Arithmetic of Weil curves

  • B. Mazur
  • P. Swinnerton-Dyer


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  1. 1.
    Atkin, A. O. L., Lehner, J.: Hecke operators onΓ 0(m). (m). Math. Ann.185, 134–160 (1970)Google Scholar
  2. 2.
    Birch, B. J.: Elliptic curves, a progress report. Proceedings of the 1969 Summer Institute on Number Theory, Stony Brook, New York, AMS, pp. 396–400 (1971)Google Scholar
  3. 3.
    Birch, B. J., Stephens, N. M.: (unpublished): But see Birch, Elliptic curves and modular functions. Symposia MathematicaIV, 27–32, Instituto Nazionale Di Alta Matematica (1970)Google Scholar
  4. 4.
    Cartier, P., Roy, Y.: Certains calculs numériques relatifs à l'interpolationp-adique des séries de Dirichlet. Vol. III of The Proceedings of the International Summer School on Modular Functions, Antwerp (1972). Lecture Notes in Mathematics350. Berlin-Heidelberg-New York: Springer 1973Google Scholar
  5. 5.
    Deligne, P.: Formes modulaires et représentationsl-adiques. Séminaire Bourbaki 68/69 no. 355. Lecture Notes in Mathematics179, pp. 136–172 Berlin-Heidelberg-New York Springer 1971Google Scholar
  6. 6.
    Deligne, P., Rapoport, M.: Schémas de modules des courbes elliptiques. Vol. II of The Proceedings of the International Summer School on Modular Functions, no. 349, Antwerp (1972). Lecture Notes in Mathematics349, Berlin-Heidelberg-New York: Springer 1973Google Scholar
  7. 7.
    Fricke, R.: Lehrbuch der Algebra. Bd. III, Braunschweig: Vieweg 1928Google Scholar
  8. 8.
    Igusa, J.: Kroneckerian models of fields of elliptic modular functions. Am. J. of Math.81, 561–577 (1959)Google Scholar
  9. 9.
    Ligozat, G.: FonctionsL des courbes modulaires. Séminaire Delange-Pisot-Poitou, Jan. 1970. See also thesis to be publishedGoogle Scholar
  10. 10.
    Manin, Y. T.: Parabolic points and zeta functions of modular forms. (Russian) Isv. Acad. Nauk., pp. 19–65 (1972)Google Scholar
  11. 11.
    Manin, Y. T.: Periods of parabolic forms andp-adic Hecke series. (Russian) preprint, to appear in Usp. Math. NaukGoogle Scholar
  12. 12.
    Mazur, B.: Courbes elliptiques et symboles modulaires. Séminaire Bourbaki, no. 414. Juin 1972Google Scholar
  13. 13.
    Mazur, B.: Rational points on abelian varieties with values in towers of number fields. Inventiones math.18, 183–266 (1972)Google Scholar
  14. 14.
    Ogg, A.: Elliptic curves and wild ramification. Am. J. Math., pp. 1–21 (1967)Google Scholar
  15. 15.
    Ogg, A.: Rational points on certain elliptic modular curves. Talk given in St. Louis on March 29, 1972 at the AMS Symposium on Analytic Number Theory and related parts of analysis, AMS, pp. 221–231 (1973)Google Scholar
  16. 16.
    Serre, J.-P.: Propriétés galoisiennes des points d'ordre fini des courbes elliptiques. Inventiones math.15, 259–331 (1972)Google Scholar
  17. 17.
    Serre, J.-P.: Formes modulaires et fonctions zêtap-adiques, vol. III of The Proceedings of the Summer Sohool on Modular Functions, Antwerp (1972). Lecture Notes in Mathematics350. Berlin-Heidelberg-New York: Springer 1973Google Scholar
  18. 18.
    Siegel, C. L.: Über die Fourierschen Koeffizienten von Modulformen. Gött. Nach.3, 15–56 (1970)Google Scholar
  19. 19.
    Shimura, G.: Introduction to the Arithmetic Theory of Automorphic Functions. Publ. Math. Soc. Japan 11, Iwanomi Shoten Publishers, and Princeton Univ. Press (1971)Google Scholar
  20. 20.
    Swinnerton-Dyer, H. P. F.: The conjectures of Birch and Swinnerton-Dyer, and of Tate. Proc. of a conference on local fields, pp. 132–157. Berlin-Heidelberg-New York: Springer 1967Google Scholar
  21. 21.
    Tate, J.: On the conjecture of Birch and Swinnerton-Dyer and a geometric analog. Séminaire Bourbaki, no. 306Google Scholar
  22. 22.
    Tate, J.: The arithmetic of elliptic curves. Distributed in conjunction with the Colloquium Lectures given at Dartmouth College. Hanover, New Hampshire, Aug. 29–Sept 1, 1972, seventy-seventh summer meeting of the American Math. Soc. Inventiones math.23, 179–206 (1974)Google Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • B. Mazur
    • 1
  • P. Swinnerton-Dyer
    • 2
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA
  2. 2.Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeCambridgeU.K.

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