manuscripta mathematica

, Volume 105, Issue 2, pp 253–263 | Cite as

Linear independence measures for infinite products

  • Peter Bundschuh
  • Keijo Väänänen


Let f be an entire transcendental function with rational coefficients in its power series about the origin. Further, let f satisfy a functional equation f(qz)= (zc)f(z)+Q(z) with \(\) and some particular c∈ℚ. Then the linear independence of 1,f(α), f(−α) over ℚ for non-zero α∈ℚ is proved, and a linear independence measure for these numbers is given. Clearly, for Q= 0 the function f can be written as an infinite product.

Mathematics Subject Classification (2000): 11J72, 11J82 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Peter Bundschuh
    • 1
  • Keijo Väänänen
    • 2
  1. 1.Mathematisches Institut der Universität zu Köln, Weyertal 86–90,¶50931 Köln, Germany. e-mail: pb@math.uni-koeln.deDE
  2. 2.Department of Mathematical Sciences, University of Oulu, PO Box 3000, 90401 Oulu, Finland. e-mail: kvaanane@sun3.oulu.fiFI

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