Advertisement

On the development of Gelfond's method

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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

Personalised recommendations