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

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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.

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References

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Author notes

  1. Keijo Väänänen

    Present address: Mathematisches Institut der Universität Freiburg, Hebelstr. 40, D-7800, Freiburg i. Br.

Authors and Affiliations

  1. Department of Mathematics, University of Oulu, SF-90100, Oulu 10, Finland

    Keijo Väänänen

Authors
  1. Keijo Väänänen
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Additional information

This work was carried out while the author was a research fellow of the Alexander von Humboldt Foundation.

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Väänänen, K. On lower bounds for polynomials in the values of E-functions. Manuscripta Math 21, 173–180 (1977). https://doi.org/10.1007/BF01168017

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  • DOI: https://doi.org/10.1007/BF01168017

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