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A note on symmetry and ambiguity

Published online by Cambridge University Press:  17 April 2009

R.A. Mollin  and
A.J. van der Poorten
R.A. Mollin
Affiliation:
School of MathematicsUniversity of CalgaryAlbertaCanada e-mail: ramollin@acs.ucalgary.ca
A.J. van der Poorten
Affiliation:
Centre for Number Theory ResearchMacquarie UniversityNew South Wales 2109Australia e-mail: alf@mpce.mq.edu.au
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Abstract

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We present the relationship between quadratic irrationals whose continued fraction expansion has symmetric period, and ambiguous ideal cycles in real quadratic number fields.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 2 , April 1995 , pp. 215 - 233
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Buell, D.A., Binary quadratic forms: classical theory and modern computations (Springer-Verlag, Berlin, Heidelbrg, New York, 1989).CrossRefGoogle Scholar
[2]Cohn, H., A second course in number theory, reprinted as Advanced number theory, (Dover Books, 1980) (Wiley, 1962).Google Scholar
[3]Dickson, L.E., Introduction to the theory of numbers (University of Chicago Press, Chicago, 1929) (reprinted by Dover Books, 1957).Google Scholar
[4]Galois, É., ‘Démonstration d'un théorème sur les fractions continues périodiques’, Ann. Mat. Pura. Appl. 19 (1828–1829), (Oeuvres de Galois [80, 83]; as cited in Oskar Perron, Sections 22–23 op. cit.), 294.Google Scholar
[5]Hardy, G.H. and Wright, E.M., An introduction to the theory of numbers (Oxford University Press).CrossRefGoogle Scholar
[6]Mathews, G.B., Theory of numbers (Chelsea, New York, 1960).Google Scholar
[7]Mollin, R.A., ‘The palindromic index — a measure of ambiguous ideal classes without ambiguous ideals in class groups of real quadratic orders’, Journal de Théorie des Nombres de Bordeaux (to appear).Google Scholar
[8]Perron, O., Die Lehre von den Kettenbrüchen, (Chelsea reprint of 1929 edition) (Teubner, Leipzig).Google Scholar
[9]Rockett, A.M. and Szüsz, P., Continued fractions (World Scientific Publishing Co., Singapore, 1992).CrossRefGoogle Scholar