Transcendence degree of some fields generated by values of the exponential function

  • Yu. V. Nesterenko


Exponential Function Transcendence Degree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    A. O. Gel'fond, “On the algebraic independence of algebraic powers of algebraic numbers,” Dokl. Akad. Nauk SSSR,64, No. 3, 277–280 (1949).Google Scholar
  2. 2.
    A. O. Gel'fond, “On the algebraic independence of transcendental numbers of certain classes,” Usp. Mat. Nauk,4, No. 5, 14–48 (1949).Google Scholar
  3. 3.
    O. Zariski and P. Samuel, Commutative Algebra, Vol. 2, van Nostrand, Princeton, N. J. (1960).Google Scholar
  4. 4.
    Yu. V. Nesterenko, “On a sufficient criterion for the algebraic independence of numbers,” Vestn. Mosk. Gos. Univ. Ser. 1, Mat. Mekh., No. 4, 63–68 (1983).Google Scholar
  5. 5.
    Yu. V. Nesterenko, “On the algebraic independence of algebraic powers of algebraic numbers,” Mat. Sb.,123 (165), No. 4, 435–459 (1984).Google Scholar
  6. 6.
    Yu. V. Nesterenko, “A measure of the algebraic independence of values of certain functions,” Mat. Sb.,128 (170). No. 12, 545–568 (1985).Google Scholar
  7. 7.
    G. Dias, “Grands degrés de transcendance pour des familles d'exponentielles,” C. R. Acad. Sci. Paris,305, Sér. I, No. 5, 159–162 (1987).Google Scholar
  8. 8.
    Yu. V. Nesterenko, “On the algebraical independence of algebraic numbers to algebraic powers,” C. R. Conference “Approximations Diophantiennes et Nombres Transcendants,” Luminy, 1982. Progress in Math.,31, 199–220 (1983).Google Scholar
  9. 9.
    P. Philippen, “Critères pour l'indépendance algébrique,” Publ. Math. IHES, No. 64, 5–52 (1986).Google Scholar
  10. 10.
    R. Tijdeman, “An auxiliary result in the theory of transcendental numbers,” J. Number Theory,5, 80–94 (1973).Google Scholar
  11. 11.
    M. Waldschmidt, Nombres Transcendants, Lecture Notes in Mathematics, Vol. 402, Springer, Berlin (1974).Google Scholar
  12. 12.
    M. Waldschmidt, “Algebraic independence of transcendental numbers. Gel'fond's method and its developments,” in: Anniversary of Oberwolfach, Perspectives in Mathematics, Birkhäuser (1984), pp. 551–571.Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • Yu. V. Nesterenko
    • 1
  1. 1.M. V. Lomonosov State UniversityUSSR

Personalised recommendations