zbMATH — the first resource for mathematics

Units in the modular function field. I. - II: A full set of units. - III: Distribution relations. (English) Zbl 0311.14005

14G25 Global ground fields in algebraic geometry
11R58 Arithmetic theory of algebraic function fields
Full Text: DOI EuDML
[1] Baker, A.: Contributions to the theory of diophantine equations. Phil. Trans. Royal Soc. London Series A, Math. and Physical Sciences No.1139, Vol. 263 (1968), pp. 173?208 · Zbl 0157.09702
[2] Baker, A., Coates, J.: Integer points on curves of genus 1. Proc. Camb. Phil. Soc.67 (1970), pp. 595?602 · Zbl 0194.07601
[3] Brylinski, J.: Torsion sur les courbes élliptiques (to appear)
[4] Chabauty, C.: Sur le théorème fondamental de la théorie des points entiers et pseudo-entiers des courbes algébriques. C. R. Acad. Sci. Paris No.217 (1943), pp. 336?338 · Zbl 0060.12101
[5] Chabauty, C.: Démonstration de quelques lemmes de rehaussement. C. R. Acad. Sci. Paris No.217 (1943), pp. 413?415 · Zbl 0063.00763
[6] Chevalley, C., Weil, A.: Un théorème d’arithmétique sur les courbes algébriques. C. R. Acad. Sci. Paris (1930), pp. 570?572
[7] Clemens, H.: On Prym varieties (to appear)
[8] Coates, J.: An effective analogue of a theorem of Thue. Acta Arithmetica, three papers:I, Vol. 15 (1969), pp. 279?305;II, Vol. 16 (1970), pp. 399?412;III, Vol. 16 (1970), pp. 425?435
[9] Deligne, P., Rapoport, M.: Les schémas de modules des courbes élliptiques. Modular functions of one variable II. Springer Lecture Notes No.349, pp. 143?316 · Zbl 0281.14010
[10] Demjanenko, V. A.: Torsion of elliptic curves. Izv. Akad. Nauk SSSR, Ser. Mat. Tom35 (1971), No. 2, AMS translation, pp. 289?318
[11] Demjanenko, V. A.: On the uniform boundedness of the torsion of elliptic curves over algebraic number fields. Izv. Akad. Nauk SSSR, Ser. Mat. Tom36 (1972), No. 3, AMS translation, pp. 477?490
[12] Grothendieck, A.: Eléments de géometrie algébrique. Pub. IHES, ChapterIV, 7.8.3, 7.8.6
[13] Drinfeld, V. G.: Two theorems on modular curves. Functional analysis and its applications, Vol.7, No. 2, translated from the Russian, April?June 1973, pp. 155?156
[14] Fricke, R.: Elliptische Funktionen und ihre Anwendungen, Vol. 1, pp. 450?451: Leipzig: Teubner Verlag 1930 · JFM 56.1006.01
[15] Gelfond, A. O.: Transcendental and algebraic numbers. Moscow, 1952; translated, Dover press, 1960 · Zbl 0090.26103
[16] Hasse, H.: Neue Begründung der komplexen Multiplikation, I and II. J. Reine Angew. Math.157 (1927), pp. 115?139 and165 (1931), pp. 64?88 · JFM 52.0377.01
[17] Hellegouarch, Y.: Une propriété arithmétique des points exceptionnels rationnels d’ordre pair d’une cubique de genre 1, C. R. Acad. Sci. Paris260 (1965), pp. 5989?5992
[18] Hellegouarch, Y.: Applications d’une propriété arithmétique des points exceptionnels d’ordre pair d’une cubique de genre 1. C. R. Acad. Sci. Paris 260 (1965), pp. 6256?6258 · Zbl 0135.09303
[19] Hellegouarch, Y.: Étude des points d’ordre fini des variétés abéliennes de dimension un definies sur un anneau principal, J. Reine angew. Math.244 (1970), pp. 20?36 · Zbl 0199.24602
[20] Hellegouarch, Y.: Points d’ordre fini sur les courbes élliptiques. C. R. Acad. Sci. Paris Ser. A?B273 (1971), pp. 540?543 · Zbl 0226.10023
[21] Iwasawa, K.: Lectures onp-adicL-functions. Annals of Math. Studies No. 74
[22] Klein, F.: Über die elliptischen Normalkurven dern-ten Ordnung und die zugehörigen Modulfunktionen dern-ten Stufe. Leipziger Abh. Bd. 13 (1885), p. 339
[23] Klein, F., Fricke, R.: Vorlesungen über die Theorie der elliptischen Modulfunktionen, Vol. 2. Johnson Reprint Corporation, NY, and Teubner Verlag, Stuttgart 1966 (from the 1890 edition)
[24] Kubert, D.: Universal bounds on the torsion of elliptic curves. J. London Math. Soc. (to appear) · Zbl 0331.14010
[25] Lang, S.: Elliptic functions. Addison Wesley, Reading (1974)
[26] Lang, S.: Integral points on curves. Pub. IHES (1960) · Zbl 0112.13402
[27] Lang, S.: Diophantine geometry. New York: Interscience 1962 · Zbl 0115.38701
[28] Lang, S.: Isogenous generic elliptic curves. Am. J. Math. 1972 · Zbl 0244.14011
[29] Leopoldt, H.: Eine Verallgemeinung der Bernoullischen Zahlen. Abh. Math. Sem. Hamburg (1958), pp. 131?140 · Zbl 0080.03002
[30] Manin. J.: Parabolic points and zeta-functions of modular curves. Izv. Akad. Nauk SSSR, Ser. Mat. Tom36 (1972), No. 1, AMS translation, pp. 19?64 · Zbl 0243.14008
[31] Mumford, D.: Prym varieties (to appear) · Zbl 0299.14018
[32] Newman, M.: Construction and application of a class of modular functions. Proc. London Math. Soc. (3)7 (1957), pp. 334?350 · Zbl 0097.28701
[33] Ramachandra, K.: Some applications of Kronecker’s limit formula. Ann. of Math.80 (1964), pp. 104?148 · Zbl 0142.29804
[34] Recillas, S.: A relation between curves of genus three and curves of genus 4. Ph. D. dissertation, Brandeis University 1970 (see especially, pp. 107?108, and Theorem 2 of Chapter IV et sequences)
[35] Robert, G.: Unités élliptiques. Bull. Soc. Math. France, Memoire No.36 (1973)
[36] Roth, P.: Über Beziehungen zwischen algebraischen Gebilden von Geschlechtern drei und vier. Monatshefte22 (1911) · JFM 42.0473.01
[37] Shimura, G.: Introduction to the arithmetic theory of automorphic functions. Iwanami Shoten and Princeton University Press 1971 · Zbl 0221.10029
[38] Siegel, C. L.: Über einige Anwendungen diophantischer Approximationen. Abh. Preuss. Akad. Wiss. Phys. Math. Kl. (1929), pp. 41?69 · JFM 56.0180.05
[39] Weil, A.: Arithmétique et géometrie sur les variétés algébriques. Act. Sci. et Ind. No.206. Paris: Hermann 1935
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.