Palindromic continued fractions

Boris Adamczewski[1]; Yann Bugeaud[2]

  • [1] CNRS and Université Claude Bernard Lyon 1 Institut Camille Jordan Bât. Braconnier, 21 avenue Claude Bernard 69622 Villeurbanne Cedex (FRANCE)
  • [2] Université Louis Pasteur U. F. R. de mathématiques 7, rue René Descartes 67084 Strasbourg Cedex (FRANCE)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 5, page 1557-1574
  • ISSN: 0373-0956

Abstract

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In the present work, we investigate real numbers whose sequence of partial quotients enjoys some combinatorial properties involving the notion of palindrome. We provide three new transendence criteria, that apply to a broad class of continued fraction expansions, including expansions with unbounded partial quotients. Their proofs heavily depend on the Schmidt Subspace Theorem.

How to cite

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Adamczewski, Boris, and Bugeaud, Yann. "Palindromic continued fractions." Annales de l’institut Fourier 57.5 (2007): 1557-1574. <http://eudml.org/doc/10270>.

@article{Adamczewski2007,
abstract = {In the present work, we investigate real numbers whose sequence of partial quotients enjoys some combinatorial properties involving the notion of palindrome. We provide three new transendence criteria, that apply to a broad class of continued fraction expansions, including expansions with unbounded partial quotients. Their proofs heavily depend on the Schmidt Subspace Theorem.},
affiliation = {CNRS and Université Claude Bernard Lyon 1 Institut Camille Jordan Bât. Braconnier, 21 avenue Claude Bernard 69622 Villeurbanne Cedex (FRANCE); Université Louis Pasteur U. F. R. de mathématiques 7, rue René Descartes 67084 Strasbourg Cedex (FRANCE)},
author = {Adamczewski, Boris, Bugeaud, Yann},
journal = {Annales de l’institut Fourier},
keywords = {Continued fractions; palindromes; transcendental numbers; Subspace Theorem; continued fractions; subspace theorem},
language = {eng},
number = {5},
pages = {1557-1574},
publisher = {Association des Annales de l’institut Fourier},
title = {Palindromic continued fractions},
url = {http://eudml.org/doc/10270},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Adamczewski, Boris
AU - Bugeaud, Yann
TI - Palindromic continued fractions
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 5
SP - 1557
EP - 1574
AB - In the present work, we investigate real numbers whose sequence of partial quotients enjoys some combinatorial properties involving the notion of palindrome. We provide three new transendence criteria, that apply to a broad class of continued fraction expansions, including expansions with unbounded partial quotients. Their proofs heavily depend on the Schmidt Subspace Theorem.
LA - eng
KW - Continued fractions; palindromes; transcendental numbers; Subspace Theorem; continued fractions; subspace theorem
UR - http://eudml.org/doc/10270
ER -

References

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