# On the period length of some special continued fractions

Journal de théorie des nombres de Bordeaux (1992)

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

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topMollin, 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

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