On Multiplicative Independent Bases for Canonical Number Systems in Cyclotomic Number Fields

  • Manfred G. Madritsch
  • Paul Surer
  • Volker Ziegler
Chapter

Abstract

In the present paper we are interested in number systems in the ring of integers of cyclotomic number fields in order to obtain a result equivalent to Cobham’s theorem. For this reason we first search for potential bases. This is done in a very general way in terms of canonical number systems. In a second step we analyse pairs of bases in view of their multiplicative independence. In the last part we state an appropriate variant of Cobham’s theorem.

2010 Mathematics Subject Classification

11R18 11Y40 11A63 

Notes

Acknowledgements

We want to explicitly give thanks to the anonymous referees. Due to their hints and suggestions we were able to improve a lot the quality and readability of this article. The second author’s research was supported by the Austrian Research Foundation (FWF), Project P23990.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Manfred G. Madritsch
    • 1
    • 2
  • Paul Surer
    • 3
  • Volker Ziegler
    • 4
  1. 1.Institut Elie Cartan de LorraineUniversité de Lorraine, UMR 7502Vandoeuvre-lès-NancyFrance
  2. 2.Institut Elie Cartan de Lorraine, CNRS, UMR 7502Vandoeuvre-lès-NancyFrance
  3. 3.Institut für MathematikUniverstiät für Bodenkultur (BOKU)WienAustria
  4. 4.Institute of MathematicsUniversity of SalzburgSalzburgAustria

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