On the quasi-periodic p -adic Ruban continued fractions

Basma Ammous; Nour Ben Mahmoud; Mohamed Hbaib

Czechoslovak Mathematical Journal (2022)

  • Volume: 72, Issue: 4, page 1157-1166
  • ISSN: 0011-4642

Abstract

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We study a family of quasi periodic p -adic Ruban continued fractions in the p -adic field ℚ p and we give a criterion of a quadratic or transcendental p -adic number which based on the p -adic version of the subspace theorem due to Schlickewei.

How to cite

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Ammous, Basma, Ben Mahmoud, Nour, and Hbaib, Mohamed. "On the quasi-periodic $p$-adic Ruban continued fractions." Czechoslovak Mathematical Journal 72.4 (2022): 1157-1166. <http://eudml.org/doc/298902>.

@article{Ammous2022,
abstract = {We study a family of quasi periodic $p$-adic Ruban continued fractions in the $p$-adic field $\mathbb \{Q\}_p$ and we give a criterion of a quadratic or transcendental $p$-adic number which based on the $p$-adic version of the subspace theorem due to Schlickewei.},
author = {Ammous, Basma, Ben Mahmoud, Nour, Hbaib, Mohamed},
journal = {Czechoslovak Mathematical Journal},
keywords = {continued fraction; $p$-adic number; transcendence; subspace theorem},
language = {eng},
number = {4},
pages = {1157-1166},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the quasi-periodic $p$-adic Ruban continued fractions},
url = {http://eudml.org/doc/298902},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Ammous, Basma
AU - Ben Mahmoud, Nour
AU - Hbaib, Mohamed
TI - On the quasi-periodic $p$-adic Ruban continued fractions
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 4
SP - 1157
EP - 1166
AB - We study a family of quasi periodic $p$-adic Ruban continued fractions in the $p$-adic field $\mathbb {Q}_p$ and we give a criterion of a quadratic or transcendental $p$-adic number which based on the $p$-adic version of the subspace theorem due to Schlickewei.
LA - eng
KW - continued fraction; $p$-adic number; transcendence; subspace theorem
UR - http://eudml.org/doc/298902
ER -

References

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  2. Adamczewski, B., Bugeaud, Y., 10.4007/annals.2007.165.547, Ann. Math. (2) 165 (2007), 547-565. (2007) Zbl1195.11094MR2299740DOI10.4007/annals.2007.165.547
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  7. Mahler, K., Zur Approximation p -adischer Irrationalzahlen, Nieuw Arch. Wiskd. 18 (1934), 22-34 German. (1934) Zbl0009.20003
  8. Maillet, E., Introduction à la théorie des nombres transcendants et des propriétés arithmétiques des fonctions, Gauthier-Villars, Paris (1906), French 9999JFM99999 37.0237.02. (1906) 
  9. Neukirch, J., 10.1007/978-3-662-03983-0, Grundlehren der Mathematischen Wissenschaften 322. Springer, Berlin (1999). (1999) Zbl0956.11021MR1697859DOI10.1007/978-3-662-03983-0
  10. Ooto, T., 10.1007/s00209-017-1859-2, Math. Z. 287 (2017), 1053-1064. (2017) Zbl1388.11040MR3719527DOI10.1007/s00209-017-1859-2
  11. Ruban, A. A., 10.1007/BF00970247, Sib. Math. J. 11 (1970), 176-180. (1970) Zbl0213.32701MR0260700DOI10.1007/BF00970247
  12. Schlickewei, H. P., 10.1007/BF01220404, Arch. Math. 29 (1977), 267-270. (1977) Zbl0365.10026MR0491529DOI10.1007/BF01220404
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  14. Wang, L., P -adic continued fractions. I, Sci. Sin., Ser. A 28 (1985), 1009-1017. (1985) Zbl0628.10036MR0866457

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