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

In: Number Theory – Diophantine Problems, Uniform Distribution and Applications

Author

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  • Manfred G. Madritsch

    (Université de Lorraine, UMR 7502, Institut Elie Cartan de Lorraine
    Institut Elie Cartan de Lorraine, CNRS, UMR 7502)

  • Paul Surer

    (Universtiät für Bodenkultur (BOKU), Institut für Mathematik)

  • Volker Ziegler

    (University of Salzburg, Institute of Mathematics)

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.

Suggested Citation

  • Manfred G. Madritsch & Paul Surer & Volker Ziegler, 2017. "On Multiplicative Independent Bases for Canonical Number Systems in Cyclotomic Number Fields," Springer Books, in: Christian Elsholtz & Peter Grabner (ed.), Number Theory – Diophantine Problems, Uniform Distribution and Applications, pages 313-332, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-55357-3_16
    DOI: 10.1007/978-3-319-55357-3_16
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