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References
Atkin, A. O. L., Lehner, J.: Hecke operators onΓ0(m). (m). Math. Ann.185, 134–160 (1970)
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)
Birch, B. J., Stephens, N. M.: (unpublished): But see Birch, Elliptic curves and modular functions.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)
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 1973
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 1971
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 1973
Fricke, R.: Lehrbuch der Algebra. Bd. III, Braunschweig: Vieweg 1928
Igusa, J.: Kroneckerian models of fields of elliptic modular functions. Am. J. of Math.81, 561–577 (1959)
Ligozat, G.: FonctionsL des courbes modulaires. Séminaire Delange-Pisot-Poitou, Jan. 1970. See also thesis to be published
Manin, Y. T.: Parabolic points and zeta functions of modular forms. (Russian) Isv. Acad. Nauk., pp. 19–65 (1972)
Manin, Y. T.: Periods of parabolic forms andp-adic Hecke series. (Russian) preprint, to appear in Usp. Math. Nauk
Mazur, B.: Courbes elliptiques et symboles modulaires. Séminaire Bourbaki, no. 414. Juin 1972
Mazur, B.: Rational points on abelian varieties with values in towers of number fields. Inventiones math.18, 183–266 (1972)
Ogg, A.: Elliptic curves and wild ramification. Am. J. Math., pp. 1–21 (1967)
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)
Serre, J.-P.: Propriétés galoisiennes des points d'ordre fini des courbes elliptiques. Inventiones math.15, 259–331 (1972)
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 1973
Siegel, C. L.: Über die Fourierschen Koeffizienten von Modulformen. Gött. Nach.3, 15–56 (1970)
Shimura, G.: Introduction to the Arithmetic Theory of Automorphic Functions. Publ. Math. Soc. Japan 11, Iwanomi Shoten Publishers, and Princeton Univ. Press (1971)
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 1967
Tate, J.: On the conjecture of Birch and Swinnerton-Dyer and a geometric analog. Séminaire Bourbaki, no. 306
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)
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Department of Mathematics, Harvard University, 02139, Cambridge, Mass., USA
B. Mazur
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, CB 2 1 SB, Cambridge, U.K.
P. Swinnerton-Dyer
- B. Mazur
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- P. Swinnerton-Dyer
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This author was a recipient of NSF Grant No. 31359X-1, and would like to thank the Institut des Hautes Etudes Scientifiques for its generous hospitality while he was engaged in the writing of this paper.
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Mazur, B., Swinnerton-Dyer, P. Arithmetic of Weil curves.Invent Math25, 1–61 (1974). https://doi.org/10.1007/BF01389997
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