ArticleOriginal scientific text

Title

Some generalizations of the Sₙ sequence of Shanks

Authors 1

Affiliations

  1. Department of Computer Science, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2NT

Bibliography

  1. T. Azuhata, On the fundamental units and the class numbers of real quadratic fields II, Tokyo J. Math. 10 (1987), 259-270.
  2. L. Bernstein, Fundamental units and cycles, J. Number Theory 8 (1976), 446-491.
  3. L. Bernstein, Fundamental units and cycles in the period of real quadratic fields, Part II , Pacific J. Math. 63 (1976), 63-78.
  4. L. E. Dickson, History of the Theory of Numbers, Vol. II, Chelsea, 1971.
  5. F. Halter-Koch, Einige periodische Kettenbruchentwicklungen und Grundeinheiten quadratischer Ordnung, Abh. Math. Sem. Univ. Hamburg 59 (1989), 157-169.
  6. F. Halter-Koch, Reell-quadratische Zahlkörper mit grosser Grundeinheit, Abh. Math. Sem. Univ. Hamburg 59 (1989), 171-181.
  7. M. D. Hendy, Applications of a continued fraction algorithm to some class number problems, Math. Comp. 28 (1974), 267-277.
  8. C. Levesque, Continued fraction expansions and fundamental units, J. Math. Phys. Sci. 22 (1988), 11-14.
  9. C. Levesque and G. Rhin, A few classes of periodic continued fractions, Utilitas Math. 30 (1986), 79-107.
  10. R. A. Mollin and H. C. Williams, Consecutive powers in continued fractions, Acta Arith. 61 (1992), 233-264.
  11. R. A. Mollin and H. C. Williams, On the period length of some special continued fractions, Sém. Théorie des Nombres de Bordeaux 4 (1992), 19-42.
  12. A. Schinzel, On some problems of the arithmetical theory of continued fractions, Acta Arith. 6 (1961), 393-413.
  13. D. Shanks, On Gauss's class number problems, Math. Comp. 23 (1969), 151-163.
  14. D. Shanks, Class number, a theory of factorization and genera, in: Proc. Sympos. Pure Math. 20, Amer. Math. Soc., Providence, R.I., 1971, 415-440.
  15. H. C. Williams, A note on the period length of the continued fraction expansion of certain √D, Utilitas Math. 28 (1985), 201-209.
  16. H. C. Williams and M. C. Wunderlich, On the parallel generation of the residues for the continued fraction factoring algorithm, Math. Comp. 48 (1987), 405-423.
  17. Y. Yamamoto, Real quadratic fields with large fundamental units, Osaka J. Math. 8 (1971), 261-270.
Pages:
199-215
Main language of publication
English
Received
1993-02-22
Published
1995
Exact and natural sciences