On the development of Gelfond's method

  • W. Dale Brownawell
Part of the Lecture Notes in Mathematics book series (LNM, volume 751)


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  1. [Br 1]
    W.D. Brownawell, The algebraic independence of certain values of the exponential function, K. norske Vidensk. Selsk. Skr., No. 23 (1972), 5p.Google Scholar
  2. [Br 2]
    —, Sequences of diophantine approximations, J. Number Th. 6 (1974), 11–21.MathSciNetCrossRefMATHGoogle Scholar
  3. [Br 3]
    —, The algebraic independence of certain numbers related by the exponential function, J. Number Th. 6 (1974), 22–31.MathSciNetCrossRefMATHGoogle Scholar
  4. [Br 4]
    —, Gelfond's method for algebraic independence, Trans. A.M.S. 210 (1975), 1–26.MathSciNetMATHGoogle Scholar
  5. [Br 5]
    —, Pairs of polynomials small at a number to certain algebraic powers, Sem. Delange Pisot Poitou, 17e année (1975/76), No. 11Google Scholar
  6. [Br 6]
    —, Some remarks on semi-resultants, Chapter 14 in Transcendence Theory: Advances and Applications, A. Baker and D.W. Masser, eds, Academic Press, London, 1977.Google Scholar
  7. [Br 7]
    —, On the Gelfond-Feldman measure of algebraic independence, Compositio Math. (to appear)Google Scholar
  8. [Br-Wald]
    W.D. Brownawell and M. Waldschmidt, The algebraic independence of certain numbers to algebraic powers, Acta Arith. 32 (1977), 63–71.MathSciNetMATHGoogle Scholar
  9. [Ca]
    J.W.S. Cassels, An Introduction to Diophantine Approximations, Cambridge University Press, Cambridge, 1957.MATHGoogle Scholar
  10. [Ch 1]
    G.V. Chudnovsky, The algebraic independence of certain values of the exponential function, Mat. Zametki 15 (1974), 661–672; Math. Notes 15 (1974), 391–398.MathSciNetGoogle Scholar
  11. [Ch 2]
    —, Some analytic methods in the theory of transcendental numbers, Ukrainian SSR Academy of Sciences, Preprint IM-74-8, Kiev, 1974, 48 p.; Analytic methods in diophantine approximations, id., IM-74-9, Kiev, 1974, 52 p.Google Scholar
  12. [Ch 3]
    —, A mutual transcendence measure for some classes of numbers, Dokl. Akad. Nauk SSSR 218 (1974), 771–774; Soviet Math. Dokl. 15 (1974), 1424–1428.MathSciNetGoogle Scholar
  13. [Ch 4]
    —, Towards the Schanuel hypothesis; algebraic curves near a point. Part I. General theory of colored sequences, 33p. Part II. Fields of finite type of transcendence and colored sequences; resultants, 23 p. (manuscript)Google Scholar
  14. [Ch 5]
    G.V. Chudnovsky, Algebraic grounds for the proof of algebraic independence. How to obtain a measure of algebraic independence using elementary methods, Part I. Elementary algebra, 30 p. (manuscript)Google Scholar
  15. [Ch 6]
    —, Explicit construction of auxiliary functions for transcendental numbers, these Proceedings.Google Scholar
  16. [Cij]
    P.L. Cijsouw, Transcendence Measures, Thesis, Amsterdam, 1972.Google Scholar
  17. [Ge]
    A.O. Gelfond, Transcendental and Algebraic Numbers, GITTL, Moscow, 1952; Dover, New York, 1960.MATHGoogle Scholar
  18. [Ge-Fe]
    A.O. Gelfond and N.I. Feldman, On the measure of relative transcendence of certain numbers, Izv. Akad. Nauk SSSR 14 (1950), 493–500.MathSciNetGoogle Scholar
  19. [La]
    S. Lang, Introduction to Transcendental Numbers, Addison-Wesley, Reading, Mass., 1966.MATHGoogle Scholar
  20. [Mi-Wald]
    M. Mignotte and M. Waldschmidt, Linear forms in logarithms and Schneider's method, Math. Ann. 231 (1978), 241–267.MathSciNetCrossRefMATHGoogle Scholar
  21. [Schn]
    Th. Schneider, Einführung in die transzendenten Zahlen, Springer, Berlin, 1957.CrossRefMATHGoogle Scholar
  22. [Sm]
    A.A. Smelev, On the method of A.O. Gelfond in the theory of transcendental numbers, Mat. Zametki 10 (1971), 415–426; Math Notes 10 (1971), 672–678.MathSciNetGoogle Scholar
  23. [Tij 1]
    R. Tijdeman, On the number of zeros of general exponential polynomials, Nederl. Akad. Wetensch. Proc. Ser. A 74 = Indag. Math. 33 (1971), 1–7.MathSciNetCrossRefMATHGoogle Scholar
  24. [Tij 2]
    —, On the algebraic independence of certain numbers, Nederl. Akad. Wetensch. Proc. Ser. A 74 = Indag. Math. 33 (1971), 146–162.MathSciNetCrossRefMATHGoogle Scholar
  25. [Tij 3]
    —, An auxiliary result in the theory of transcendental numbers, J. Number Th. 5 (1973), 80–94.MathSciNetCrossRefMATHGoogle Scholar
  26. [Wald 1]
    M. Waldschmidt, Solution d'un problème de Schneider sur les nombres transcendants, C.R. Acad. Sci. Ser. A-B. 271 (1970), A697–700.MathSciNetMATHGoogle Scholar
  27. [Wald 2]
    —, Indépendance algébrique des valeurs de la fonction exponentielle, Bulletin Soc. Math. France 99 (1971), 285–304.MathSciNetMATHGoogle Scholar
  28. [Wald 3]
    —, Solution du huitième probleme de Schneider, J. Number Th. 5 (1973), 191–202.MathSciNetCrossRefMATHGoogle Scholar
  29. [Wald 4]
    —, Indépendance algébrique par la methode de G.V. Chudnovsky, Sem. Delange Pisot Poitou, 16e annee (1974/75), No. G8, 18 pGoogle Scholar
  30. [Wald 5]
    M. Waldschmidt, Les travaux de G.V. Chudnovsky sur les nombres transcendants, Sem. Bourbaki, 28e annee, 1975/76, No. 488, 15 p.Google Scholar
  31. [Wall]
    R. Wallisser, reported in Review 10021, Zbl. Math. 241 (1973), 45–46 by P. Bundschuh.Google Scholar
  32. [War]
    P. Warkentin, Algebraische Unabhängigkeit gewisser p-adischer Zahlen, Diplomarbeit, Freiburg, 1978.Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • W. Dale Brownawell
    • 1
  1. 1.Department of MathematicsPennsylvannia State UniversityUniversity Park

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