Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 52: Issue 3
Some quadratic irrationals with explicit continued fraction and Engel series expansions
Authors:
Narakorn Rompurk Kanasri Khon Kaen University, Khon Kaen 40002, Thailand
CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

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,
Vichian Laohakosol Kasetsart University, Bangkok 10900, Thailand

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, and
Tawat Changphas Khon Kaen University, Khon Kaen 40002, Thailand
CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

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Pages:
316–336
Online Publication Date:
Sep 2015
Publication Date:
01 Sep 2015
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2015.52.3.1312
Keywords:
Primary 11A67; 11A55; Quadratic irrationals; Engel series; continued fractions
Restricted access

A remarkable class of quadratic irrational elements having both explicit Engel series and continued fraction expansions in the field of Laurent series, mimicking the case of real numbers discovered by Sierpiński and later extended by Tamura, is constructed. Linear integer-valued polynomials which can be applied to construct such class are determined. Corresponding results in the case of real numbers are mentioned.

  • [1]

    Knopfmacher, A. and Knopfmacher, J., Series expansions in p-adic and other non-archimedean fields, J. Number Theory, 32 (1989), 297–306.

    • Search Google Scholar
    • Export Citation
  • [2]

    Laohakosol, V. , Bases for integer-valued polynomials in a Galois field, Acta Arith., LXXXVII.1 (1998), 13–26.

  • [3]

    Laohakosol, V. and Ubolsri, P., p-adic continued fractions of Liouville type, Proc. Amer. Math. Soc., 101(3) (1987), 403–410.

  • [4]

    Laohakosol, V., Rompurk, N. and Harnchoowong, A., Characterizing rational elements using Knopfmachers’ expansions in the field of Laurent series over a finite field, Thai J. Math., 4 (2006), 223–244.

    • Search Google Scholar
    • Export Citation
  • [5]

    Liardet, P. et Stambul, P. , Séries de Engel et fractions continuées, J. Théor. Nombres Bordeaux, 12 (2000), 37–68.

  • [6]

    Mahler, K. , Zur Approximation p-adischer Irrationalzahlen, Nieuw Arch. Wisk., 18 (1934), 22–34.

  • [7]

    Perron, O. , Irrationalzahlen, Chelsea, New York, 1951.

  • [8]

    Pólya G. and Szegö, G., Problems and Theorems in Analysis, Volume II, Springer, New York–Heidelberg–Berlin, 1976.

  • [9]

    Ruban, A. , Certain metric properties of the p-adic numbers, Sibirsk. Mat. Zh., 11 (1971), 222–227; English transl. Siberian Math. J., 11 (1971), 176–180.

    • Search Google Scholar
    • Export Citation
  • [10]

    Schmidt, W. M. , On continued fractions and diophantin approximation in power series fields, Acta Arith., 95 (2000), 139–166.

  • [11]

    Sierpiński, W. , Elementary theory of Numbers, North-Holland, Amsterdam–New York–Oxford, 1988.

  • [12]

    Tamura, J. , Explicit formulae for Cantor series representing quadratic irrationals, Number Theory and Combinatorics, Japan, World Scientific Publishing Co. (1984), 369–381.

    • Search Google Scholar
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Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

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Gábor SÁGI (Rényi Institute of Mathematics)

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  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
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  • Joshua GREENE (Boston College)
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  • Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation		 1966
Volumes
per Year		 1
Issues
per Year		 4
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)

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