Geodesic
On the period length of some special continued fractions
Journal de théorie des nombres de Bordeaux, Série 2, Tome 4 (1992) no. 1, pp. 19-42.

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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.

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Mollin, R. A.; Williams, H. C. On the period length of some special continued fractions. Journal de théorie des nombres de Bordeaux, Série 2, Tome 4 (1992) no. 1, pp. 19-42. http://geodesic.mathdoc.fr/item/JTNB_1992__4_1_19_0/

[1] L. Bernstein, Fundamental units and cycles, J. Number Theory 8 (1976), 446-491. | Zbl | MR

[2] D.E. Knuth, The Art of Computer Programing II: Seminumerical Algorithms, Addison-Wesley, 1981. | MR

[3] R.A. Mollin and H.C. Williams, Consecutive powers in continued fractions, (to appear: Acta Arithmetica). | Zbl

[4] O. Perron, Die Lehre von den Kettenbrüchen, Chelsea, New-York (undated).

[5] J.W. Porter, On a theorem of Heilbronn, Mathematika 22 (1975), 20-28. | Zbl | MR