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Arithmetic of Weil curves. (English) Zbl 0281.14016

MSC:
14H45Special curves and curves of low genus
14G05Rational points
14H10Families, algebraic moduli (curves)
References:
[1]Atkin, A. O. L., Lehner, J.: Hecke operators on? 0(m). (m). Math. Ann.185, 134-160 (1970) · Zbl 0185.15502 · doi:10.1007/BF01359701
[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)
[3]Birch, B. J., Stephens, N. M.: (unpublished): But see Birch, Elliptic curves and modular functions.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)
[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 1973
[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 1971
[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 1973
[7]Fricke, R.: Lehrbuch der Algebra. Bd. III, Braunschweig: Vieweg 1928
[8]Igusa, J.: Kroneckerian models of fields of elliptic modular functions. Am. J. of Math.81, 561-577 (1959) · Zbl 0093.04502 · doi:10.2307/2372914
[9]Ligozat, G.: FonctionsL des courbes modulaires. Séminaire Delange-Pisot-Poitou, Jan. 1970. See also thesis to be published
[10]Manin, Y. T.: Parabolic points and zeta functions of modular forms. (Russian) Isv. Acad. Nauk., pp. 19-65 (1972)
[11]Manin, Y. T.: Periods of parabolic forms andp-adic Hecke series. (Russian) preprint, to appear in Usp. Math. Nauk
[12]Mazur, B.: Courbes elliptiques et symboles modulaires. Séminaire Bourbaki, no. 414. Juin 1972
[13]Mazur, B.: Rational points on abelian varieties with values in towers of number fields. Inventiones math.18, 183-266 (1972) · Zbl 0245.14015 · doi:10.1007/BF01389815
[14]Ogg, A.: Elliptic curves and wild ramification. Am. J. Math., pp. 1-21 (1967)
[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)
[16]Serre, J.-P.: Propriétés galoisiennes des points d’ordre fini des courbes elliptiques. Inventiones math.15, 259-331 (1972) · Zbl 0235.14012 · doi:10.1007/BF01405086
[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 1973
[18]Siegel, C. L.: Über die Fourierschen Koeffizienten von Modulformen. Gött. Nach.3, 15-56 (1970)
[19]Shimura, G.: Introduction to the Arithmetic Theory of Automorphic Functions. Publ. Math. Soc. Japan 11, Iwanomi Shoten Publishers, and Princeton Univ. Press (1971)
[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 1967
[21]Tate, J.: On the conjecture of Birch and Swinnerton-Dyer and a geometric analog. Séminaire Bourbaki, no. 306
[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) · Zbl 0296.14018 · doi:10.1007/BF01389745