On the period length of some special continued fractions

R. A. Mollin; H. C. Williams

Journal de théorie des nombres de Bordeaux (1992)

  • Volume: 4, Issue: 1, page 19-42
  • ISSN: 1246-7405

Abstract

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We investigate and refine a device which we introduced in [3] for the study of continued fractions. This allows us to more easily compute the period lengths of certain continued fractions and it can be used to suggest some aspects of the cycle structure (see [1]) within the period of certain continued fractions related to underlying real quadratic fields.

How to cite

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Mollin, R. A., and Williams, H. C.. "On the period length of some special continued fractions." Journal de théorie des nombres de Bordeaux 4.1 (1992): 19-42. <http://eudml.org/doc/93554>.

@article{Mollin1992,
abstract = {We investigate and refine a device which we introduced in [3] for the study of continued fractions. This allows us to more easily compute the period lengths of certain continued fractions and it can be used to suggest some aspects of the cycle structure (see [1]) within the period of certain continued fractions related to underlying real quadratic fields.},
author = {Mollin, R. A., Williams, H. C.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {period length; continued fraction expansion},
language = {eng},
number = {1},
pages = {19-42},
publisher = {Université Bordeaux I},
title = {On the period length of some special continued fractions},
url = {http://eudml.org/doc/93554},
volume = {4},
year = {1992},
}

TY - JOUR
AU - Mollin, R. A.
AU - Williams, H. C.
TI - On the period length of some special continued fractions
JO - Journal de théorie des nombres de Bordeaux
PY - 1992
PB - Université Bordeaux I
VL - 4
IS - 1
SP - 19
EP - 42
AB - We investigate and refine a device which we introduced in [3] for the study of continued fractions. This allows us to more easily compute the period lengths of certain continued fractions and it can be used to suggest some aspects of the cycle structure (see [1]) within the period of certain continued fractions related to underlying real quadratic fields.
LA - eng
KW - period length; continued fraction expansion
UR - http://eudml.org/doc/93554
ER -

References

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  1. [1] L. Bernstein, Fundamental units and cycles, J. Number Theory8 (1976), 446-491. Zbl0352.10002MR419406
  2. [2] D.E. Knuth, The Art of Computer Programing II: Seminumerical Algorithms, Addison-Wesley, 1981. MR633878
  3. [3] R.A. Mollin and H.C. Williams, Consecutive powers in continued fractions, (to appear: Acta Arithmetica). Zbl0764.11010
  4. [4] O. Perron, Die Lehre von den Kettenbrüchen, Chelsea, New-York (undated). Zbl43.0283.04
  5. [5] J.W. Porter, On a theorem of Heilbronn, Mathematika22 (1975), 20-28. Zbl0316.10019MR498452

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