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Czechoslovak Mathematical Journal

, Volume 62, Issue 3, pp 613–623 | Cite as

A note on the transcendence of infinite products

  • Jaroslav HančlEmail author
  • Ondřej Kolouch
  • Simona Pulcerová
  • Jan Štěpnička
Article
  • 96 Downloads

Abstract

The paper deals with several criteria for the transcendence of infinite products of the form \(\prod\limits_{n = 1}^\infty {[{b_n}{a^{{a_n}}}]/{b_n}{a^{{a_n}}}} \) where α > 1 is a positive algebraic number having a conjugate α* such that α ≠ |α*| > 1, {a n } n=1 and {b n } n=1 are two sequences of positive integers with some specific conditions.

The proofs are based on the recent theorem of Corvaja and Zannier which relies on the Subspace Theorem (P.Corvaja, U.Zannier: On the rational approximation to the powers of an algebraic number: solution of two problems of Mahler and Mend`es France, Acta Math. 193, (2004), 175–191).

Keywords

transcendence infinite product 

MSC 2010

11J81 

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References

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2012

Authors and Affiliations

  • Jaroslav Hančl
    • 1
    Email author
  • Ondřej Kolouch
    • 2
  • Simona Pulcerová
    • 3
  • Jan Štěpnička
    • 2
  1. 1.Department of Mathematics and Centre of Excellence IT4Innovation, division of UO, Institute for Research and Applications of Fuzzy ModelingUniversity of OstravaOstrava 1Czech Republic
  2. 2.University of OstravaOstrava 1Czech Republic
  3. 3.Department of Mathematical Methods in Economics, Faculty of EconomicsVŠB-Technical University of OstravaOstrava 1Czech Republic

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