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Algebraic Independence Results Related to 〈q, r〉-Number Systems

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Abstract.

We define 〈q, r〉-linear arithmetical functions attached to the 〈q, r〉-number systems and give a necessary and sufficient condition for their generating power series to be algebraically independent over \({\Bbb C}(z)\). We also deduce algebraic independence of the functions values at a nonzero algebraic number in the circle of convergence.

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Authors and Affiliations

  1. Keio University, Yokohama, Japan

    Shin-ichiro Okada & Iekata Shiokawa

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  1. Shin-ichiro Okada
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  2. Iekata Shiokawa
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Okada, Si., Shiokawa, I. Algebraic Independence Results Related to 〈q, r〉-Number Systems. Mh Math 147, 319–335 (2006). https://doi.org/10.1007/s00605-005-0320-5

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  • DOI: https://doi.org/10.1007/s00605-005-0320-5

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