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Fields of large transcendence degree generated by values of elliptic functions

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References

  1. Anderson, M., Masser, D.W.: Lower bounds for heights on elliptic curves. Math. Z.174, 23–34 (1980)

    Google Scholar 

  2. Borel, A.: Linear algebraic groups. New York: Benjamin 1969

    Google Scholar 

  3. Brownawell, W.D.: On the orders of zero of certain functions. Mém. Soc. Math. France2, 5–20 (1980)

    Google Scholar 

  4. Brownawell, W.D., Masser, D.W.: Multiplicity estimates for analytic functions II. Duke Math. J.47, 273–295 (1980)

    Google Scholar 

  5. Cassels, J.W.S.: An introduction to the geometry of numbers. Berlin-Göttingen-Heidelberg: Springer 1959

    Google Scholar 

  6. Chudnovsky, G.V.: Analytic methods in diophantine approximation. Kiev Preprints I.M. 74.8 and 74.9 (1974)

  7. Chudnovsky, G.V.: Algebraic independance of values of the exponential and elliptic functions, Proceedings of the International Congress of Math. Vol. 1, pp. 339–350. Helsinki 1978

    Google Scholar 

  8. Chudnovsky, G.V.: Indépendance algébrique dans la méthode de Gelfond-Schneider. C.R. Acad. Sci. Paris291A, 365–368 (1980)

    Google Scholar 

  9. Gelfond, A.O.: Transcendental and algebraic numbers. New York: Dover 1960

    Google Scholar 

  10. Hartshorne, R.: Algebraic geometry. Berlin-Heidelberg-New York: Springer 1977

    Google Scholar 

  11. Hermann, G.: Die Frage der endlich vielen Schritte in der Theorie der Polynomideale. Math. Ann.95, 736–788 (1926)

    Google Scholar 

  12. Kolchin, E.R.: Algebraic groups and algebraic dependence. Amer. J. Math.90, 1151–1164 (1968)

    Google Scholar 

  13. Lazard, D.: Algèbre linéaire surK[X 1,...,X n ] et élimination. Bull. Soc. Math. France105 165–190 (1977)

    Google Scholar 

  14. Masser, D.W.: Small values of the quadratic part of the Néron-Tate height, Progress in Math. Vol. 12, pp. 213–222. Boston-Basel-Stuttgart: Birkhäuser 1981

    Google Scholar 

  15. Masser, D.W.: On polynomials and exponential polynomials in several complex variables. Invent. Math.63, 81–95 (1981)

    Google Scholar 

  16. Masser, D.W.: A vanishing theorem for power series. Invent. Math.67, 275–296 (1982)

    Google Scholar 

  17. Masser, D.W., Wüstholz, G.: Zero estimates on group varieties I. Invent. Math.64, 489–516 (1981)

    Google Scholar 

  18. Masser, D.W., Wüstholz, G.: Algebraic independence properties of values of elliptic functions, to appear in the Proceedings of the Exeter Journées Arithmétiques 1980 (ed. J.V. Armìtage), L.M.S. Lecture Nótes No. 56, Cambridge 1982

  19. Philippon, P.: Indépendance algébrique de valeurs de fonctions exponentiellesp-adiques. J. reine angew. Math.329, 42–51 (1981)

    Google Scholar 

  20. Ramachandra, K.: Contributions to the theory of transcendental numbers I, II. Acta Arith.14, 65–88 (1968)

    Google Scholar 

  21. Reyssat, E.: Un critère d'indépendance algébrique. J. reine angew. Math.329, 66–81 (1981)

    Google Scholar 

  22. Seidenberg, A.: Constructions in algebra. Trans. Amer. Math. Soc.197, 273–313 (1974)

    Google Scholar 

  23. Tijdeman, R.: On the number of zeros of general exponential polynomials. Indag. Math.33, 1–7 (1971)

    Google Scholar 

  24. Tijdeman, R.: An auxiliary result in the theory of transcendental numbers. J. Number Th.5, 80–94 (1973)

    Google Scholar 

  25. Waldschmidt, M.: Nombres transcendants et groupes algébriques. Astérisque69–70 (1979)

  26. Zariski, O., Samuel, P.: Commutative algebra Vol. II. Berlin-Heidelberg-New York: Springer 1968

    Google Scholar 

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Masser, D.W., Wüstholz, G. Fields of large transcendence degree generated by values of elliptic functions. Invent Math 72, 407–464 (1983). https://doi.org/10.1007/BF01398396

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