×

zbMATH — the first resource for mathematics

Variétés abeliennes et independance algébrique. I. (French) Zbl 0503.10024

MSC:
11J85 Algebraic independence; Gel’fond’s method
14H52 Elliptic curves
14K15 Arithmetic ground fields for abelian varieties
14K22 Complex multiplication and abelian varieties
33E05 Elliptic functions and integrals
Citations:
Zbl 0498.14009
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Bertrand, D.: Transcendence properties of abelian integrals. Queen’s Papers in Pure and Applied Math.54, 309-318 (1980)
[2] Bertrand, D.: Sous-groupes à un paramètrep-adique. Invent. math.40, 171-193 (1977) · Zbl 0358.10016
[3] Brownawell, W.D., Kubota, K.K.: The algebraic independence of Weierstrass functions and some related numbers. Acta Arithm.33, 111-149 (1977) · Zbl 0356.10027
[4] Choodnovsky, G.V.: The Gelfond-Baker method in problems of Diophantine Approximation. Topics in Number Theory. Debrecen13, 19-30 (1974)
[5] Choodnovsky, G.V.: Algebraic independence of values of exponential and elliptic functions. Proc. Int. Congress of Math., Helsinki 1978, pp. 339-350
[6] Choodnovsky, G.V.: Algebraic independence of the values of elliptic functions at algebraic points. Invent. math.61, 267-290 (1980) · Zbl 0434.10024
[7] Dvornicich, R.: A criterion for the algebraic dependence of two complex numbers. Bollettino U.M.I.15-A, 678-687 (1978) · Zbl 0393.10039
[8] Laurent, M.: Indépendance algébrique de nombres de Liouville élevés à des puissances algébriques. C. R. Acad. Sci. Paris, Ser. A, t.286, 131-133 (1978)
[9] Macaulay, F.S.: The algebraic theory of modular systems. New York and London: Steckert-Hafner Service Agency 1964
[10] Masser, D.W., Wüstholz, G.: Zero estimates on group varieties. Invent. math.64, 489-516 (1981) · Zbl 0467.10025
[11] Masser, D.W., Wüstholz, G.: Algebraic independence properties of values of elliptic functions. Journées Arith. d’Exeter (1980), London M.S. Lecture Notes. · Zbl 0577.10034
[12] Masser, D.W., Wüstholz, G.: On large transcendence degree. (manuscrit) · Zbl 0516.10027
[13] Philippon, P.: Indépendance algébrique de valeurs de fonctionsp-adiques. J. für die Reine und Angew. Math.329, 42-51 (1981) · Zbl 0459.10024
[14] Philippon, P.: Indépendance algébrique et variétés abéliennes. C.R. Acad. Sci. Paris, Ser. I, t.294, 257-259 (1982)
[15] Reyssat, E.: Un critère d’indépendance algébrique. J. für die Reine und Angew. Math.329, 66-81 (1981) · Zbl 0459.10023
[16] Schneider, T.: Einführung in die Transzendenten Zahlen. Grundlehren der Math. Wiss, vol. 81. Berlin-Heidelberg-New York: Springer 1957; Gauthiers-Villars 1959 · Zbl 0077.04703
[17] Siegel, C.L.: Transcendental numbers. Ann. of Math. Studies, Princeton, no 16, 102pp (1949) · Zbl 0039.04402
[18] Waldschmidt, M.: Nombres transcendants et groupes algébriques. Astérisque 69-70 (1979)
[19] Waldschmidt, M.: Nombres transcendants. Lecture Notes in Mathematics, vol. 402. Berlin-Heidelberg-New York: Springer 1974 · Zbl 0302.10030
[20] Warkentin, P.: Algebraische Unabhängigkeit gewisserp-adischer Zahlen. Diplomarbeit Freiburg (1978).
[21] Weierstrass, K.: Zu Lindemanns Abhandlung: ?Über die Ludolphsche Zahl?. Sitzgsber. Preuss. Akad. Wiss. pp. 1067-1085 (1885) · JFM 17.0414.01
[22] Weil, A.: Sur les fonctions elliptiquesp-adiques. C. R. Acad. Sci. Paris, t.203, 22-24 (1936) · JFM 62.0119.03
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.