Advertisement

manuscripta mathematica

, Volume 21, Issue 2, pp 173–180 | Cite as

On lower bounds for polynomials in the values of E-functions

  • Keijo Väänänen
Article

Abstract

The paper considers polynomials in α,f1(α),...,fs(α), where α is an algebraic number satisfying certain conditions and f1(z),...,fs(z) are some E-functions, algebraically independent over the field of rational functions. Explicit lower bounds in terms of the heights of α and the polynomial are obtained for the absolute values of these polynomials. The result is proved by using the method of Siegel and Šidlovskii.

Keywords

Lower Bound Rational Function Number Theory Algebraic Geometry Topological Group 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    GALOCHKIN, A.I.: Estimate of the conjugate transcendence for the values of E-functions.(Russian) Matem. Zametki 3, No. 4, 377–386 (1968). English translation: Math. Notes 3, No. 3–4, 240–246 (1968).Google Scholar
  2. [2]
    — On the algebraic independence of the values of E-functions at some transcendental points. (Russian) Vestnik Moscov. Univ., Ser. I, No. 5, 58–63 (1970).Google Scholar
  3. [3]
    LANG, S.: Introduction to transcendental numbers. Addison-Wesley, Reading, Mass. 1966.Google Scholar
  4. [4]
    MORENO, C.J.: The values of exponential polynomials at algebraic points (I). Trans. Amer. Math. Soc. 186, 17–31 (1974).Google Scholar
  5. [5]
    -The values of exponential polynomials at algebraic points (II). Diophantine approximation and its applications, ed. by C.F. Osgood, Academic Press, 111–128 (1973).Google Scholar
  6. [6]
    ŠIDLOVSKII, A.B.: On a criterian for the algebraic independence of the values of a class of entire functions. (Russian) Izv. Akad. Nauk SSSR, Ser. Mat. 23, 35–66 (1959). English translation: Amer. Math. Soc. Transl., Vol. 22, 339–370 (1962).Google Scholar
  7. [7]
    SIEGEL, C.L.: Transcendental numbers. Princeton Univ. Press, Princeton 1949.Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Keijo Väänänen
    • 1
  1. 1.Department of MathematicsUniversity of OuluOulu 10Finland

Personalised recommendations