Number of digit changes in \({\beta}\) -expansion of unity in 详细信息    查看全文
  • 作者:M. Hbaib (1)
    Y. Laabidi (1)
    M. Merkhi (1)

    1. Dpartement de Mathmatiques
    ; Universit de Sfax ; Facult茅 des Sciences ; BP 1171 ; Sfax ; 3000 ; Tunisie
  • 关键词:formal power series ; $${\beta}$$ 尾 ; expansion ; algebraic series ; number of digit changes ; 11R06 ; 37B50
  • 刊名:Acta Mathematica Hungarica
  • 出版年:2015
  • 出版时间:April 2015
  • 年:2015
  • 卷:145
  • 期:2
  • 页码:350-359
  • 全文大小:304 KB
  • 参考文献:1. Boyd, D. (1996) On beta expansions for Pisot numbers. Math. Comp. 65: pp. 841-860 CrossRef
    2. Y., Bugeaud (2009) On the 尾-expansion of an algebraic number in algebraic base 尾. Integers 9: pp. 215-226
    3. Hbaib, M., Mkaouar, M. (2006) Sur le b锚ta-dveloppement de 1 dans le corps des sries formelles. Int. J. Number Theory 2: pp. 365-377 CrossRef
    4. Kedlaya, K.S. (2001) The algebraic closure of the power series field in positive characteristic. Proc. Amer. Math. Soc. 12: pp. 3461-3470 CrossRef
    5. J. Neukirch, / Algebraic Number Theory, The Grundlehren der Mathematischen Wissenshaften [Fondamental Principles of Mathematical Sciences]. Springer-Verlag (Berlin, 1999), 322聽pp.
    6. Parry, W. (1960) On the 尾 expansions of real numbers. Acta. Math. Acad. Sci. Hungar. 11: pp. 401-416 CrossRef
    7. Rnyi, A. (1957) Representations for real numbers and their ergodic properties. Acta. Math. Acad. Sci. Hungar. 8: pp. 477-493 CrossRef
  • 刊物类别:Mathematics and Statistics
  • 刊物主题:Mathematics
    Sciences
    Mathematics
  • 出版者:Akadmiai Kiad贸, co-published with Springer Science+Business Media B.V., Formerly Kluwer Academic
  • ISSN:1588-2632
文摘
Let \({\beta}\) be an algebraic power series over a finite field \({\mathbb{F}_{q}}\) such that \({\beta}\) is not Pisot or Salem series. We study the asymptotic behaviour of the function that counts the number of digit changes in the \({\beta}\) -expansion of 1. As a consequence, we get a transcendence criterion in \({\mathbb{F}_{q}(x)}\) .

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