×

zbMATH — the first resource for mathematics

Diophantine equations and modular forms. (English) Zbl 0316.14012

MSC:
14H45 Special algebraic curves and curves of low genus
14G05 Rational points
11F03 Modular and automorphic functions
PDF BibTeX Cite
Full Text: DOI
References:
[1] J. W. S. Cassels, Diophantine equations with special reference to elliptic curves, J. London Math. Soc. 41 (1966), 193 – 291. · Zbl 0138.27002
[2] P. Deligne and M. Rapoport, Les schémas de modules de courbes elliptiques, Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972) Springer, Berlin, 1973, pp. 143 – 316. Lecture Notes in Math., Vol. 349 (French).
[3] Max Deuring, Die Typen der Multiplikatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Hansischen Univ. 14 (1941), 197 – 272 (German). · Zbl 0025.02003
[4] Jun-ichi Igusa, Kroneckerian model of fields of elliptic modular functions, Amer. J. Math. 81 (1959), 561 – 577. · Zbl 0093.04502
[5] Daniel Sion Kubert, Universal bounds on the torsion of elliptic curves, Proc. London Math. Soc. (3) 33 (1976), no. 2, 193 – 237. · Zbl 0331.14010
[6] B. Mazur, Modular curves and the Eisenstein ideal (in preparation). · Zbl 0394.14008
[7] B. Mazur and P. Swinnerton-Dyer, Arithmetic of Weil curves, Invent. Math. 25 (1974), 1 – 61. · Zbl 0281.14016
[8] B. Mazur and J. Tate, Points of order 13 on elliptic curves, Invent. Math. 22 (1973/74), 41 – 49. · Zbl 0268.14009
[9] A. P. Ogg, Rational points of finite order on elliptic curves, Invent. Math. 12 (1971), 105 – 111. · Zbl 0216.05602
[10] A. P. Ogg, Rational points on certain elliptic modular curves, Analytic number theory (Proc. Sympos. Pure Math., Vol XXIV, St. Louis Univ., St. Louis, Mo., 1972) Amer. Math. Soc., Providence, R.I., 1973, pp. 221 – 231.
[11] A. P. Ogg, Rational points on certain elliptic modular curves, Analytic number theory (Proc. Sympos. Pure Math., Vol XXIV, St. Louis Univ., St. Louis, Mo., 1972) Amer. Math. Soc., Providence, R.I., 1973, pp. 221 – 231.
[12] Goro Shimura, Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, No. 11. Iwanami Shoten, Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1971. Kanô Memorial Lectures, No. 1. · Zbl 0221.10029
[13] Hideo Wada, A table of Hecke operators. II, Proc. Japan Acad. 49 (1973), 380 – 384. · Zbl 0273.10019
[14] A. Weil, Sur les courbes algébriques et les variétés qui s’en déduisent, Actualités Sci. Indust., no. 1041 = Publ. Inst. Math. Univ. Strasbourg 7 (1945), Hermann, Paris, 1948. MR 10, 262. · Zbl 0036.16001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.