Advertisement

The Ramanujan Journal

, Volume 30, Issue 1, pp 117–123 | Cite as

On Tschakaloff, q-exponential and related functions

  • Keijo Väänänen
Article
  • 99 Downloads

Abstract

We give a new proof for some recent interesting results of Bézivin on linear independence of the values of the functions mentioned in the title. Our results also partly generalize Bézivin’s statements and contain quantitative linear independence measures.

Keywords

Linear independence measure Tschakaloff function q-Exponential function 

Mathematics Subject Classification (2000)

11J72 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Amou, M., Matala-aho, T., Väänänen, K.: On Siegel–Shidlovskii’s theory for q-difference equations. Acta Arith. 127, 309–335 (2007) MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Bézivin, J.-P.: Indépendance linéaire des valeurs des solutions transcendantes de certaines équations fonctionnelles. Manuscr. Math. 6, 103–129 (1988) CrossRefGoogle Scholar
  3. 3.
    Bézivin, J.-P.: Indépendance linéaire des valeurs des solutions transcendantes de certaines équations fonctionnelles II. Acta Arith. 55, 233–240 (1990) MathSciNetMATHGoogle Scholar
  4. 4.
    Bézivin, J.-P.: Fonction de Tschakaloff et fonction q-exponentielle. Acta Arith. 139, 377–393 (2009) MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Bundschuh, P.: Arithmetical properties of the solutions of certain functional equations. In: Number Theory, Turku, 1999, pp. 25–42. de Gruyter, Berlin (2001) Google Scholar
  6. 6.
    Rochev, I.: New linear independence measures for values of q-hypergeometric series. arXiv:1006.5413v1 [math.NT] (2010)

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of OuluOulun yliopistoFinland

Personalised recommendations