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Reducible cubic CNS polynomials

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Abstract

The concept of a canonical number system can be regarded as a natural generalization of decimal representations of rational integers to elements of residue class rings of polynomial rings. Generators of canonical number systems are CNS polynomials which are known in the linear and quadratic cases, but whose complete description is still open. In the present note reducible CNS polynomials are treated, and the main result is the characterization of reducible cubic CNS polynomials.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Niigata University, Ikarashi 2-8050, Niigata, 950-2181, Japan

    Shigeki Akiyama

  2. Haus-Endt-Strasse 88, D-40593, Düsseldorf, Germany

    Horst Brunotte

  3. Department of Computer Science, University of Debrecen, P.O. Box 12, H-4010, Debrecen, Hungary

    Attila Pethő

Authors
  1. Shigeki Akiyama
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  2. Horst Brunotte
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  3. Attila Pethő
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Corresponding author

Correspondence to Shigeki Akiyama.

Additional information

Communicated by András Sárközy

Supported by the Japanese Ministry of Education, Culture, Sports, Science and Technology, Grand-in Aid for fundamental research 18540022, 2006–2008.

Supported partially by the Hungarian NFSR Grant No. K67580.

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Akiyama, S., Brunotte, H. & Pethő, A. Reducible cubic CNS polynomials. Period Math Hung 55, 177–183 (2007). https://doi.org/10.1007/s10998-007-4177-y

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  • DOI: https://doi.org/10.1007/s10998-007-4177-y

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