Some generalizations of the Sₙ sequence of Shanks

H. C. Williams

Acta Arithmetica (1995)

  • Volume: 69, Issue: 3, page 199-215
  • ISSN: 0065-1036

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H. C. Williams. "Some generalizations of the Sₙ sequence of Shanks." Acta Arithmetica 69.3 (1995): 199-215. <http://eudml.org/doc/206683>.

@article{H1995,
author = {H. C. Williams},
journal = {Acta Arithmetica},
keywords = {Shanks sequence ks; continued fraction expansion},
language = {eng},
number = {3},
pages = {199-215},
title = {Some generalizations of the Sₙ sequence of Shanks},
url = {http://eudml.org/doc/206683},
volume = {69},
year = {1995},
}

TY - JOUR
AU - H. C. Williams
TI - Some generalizations of the Sₙ sequence of Shanks
JO - Acta Arithmetica
PY - 1995
VL - 69
IS - 3
SP - 199
EP - 215
LA - eng
KW - Shanks sequence ks; continued fraction expansion
UR - http://eudml.org/doc/206683
ER -

References

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  1. [1] T. Azuhata, On the fundamental units and the class numbers of real quadratic fields II, Tokyo J. Math. 10 (1987), 259-270. Zbl0659.12008
  2. [2] L. Bernstein, Fundamental units and cycles, J. Number Theory 8 (1976), 446-491. Zbl0352.10002
  3. [3] L. Bernstein, Fundamental units and cycles in the period of real quadratic fields, Part II , Pacific J. Math. 63 (1976), 63-78. Zbl0335.10011
  4. [4] L. E. Dickson, History of the Theory of Numbers, Vol. II, Chelsea, 1971. 
  5. [5] F. Halter-Koch, Einige periodische Kettenbruchentwicklungen und Grundeinheiten quadratischer Ordnung, Abh. Math. Sem. Univ. Hamburg 59 (1989), 157-169. 
  6. [6] F. Halter-Koch, Reell-quadratische Zahlkörper mit grosser Grundeinheit, Abh. Math. Sem. Univ. Hamburg 59 (1989), 171-181. Zbl0718.11054
  7. [7] M. D. Hendy, Applications of a continued fraction algorithm to some class number problems, Math. Comp. 28 (1974), 267-277. Zbl0275.12007
  8. [8] C. Levesque, Continued fraction expansions and fundamental units, J. Math. Phys. Sci. 22 (1988), 11-14. Zbl0645.10010
  9. [9] C. Levesque and G. Rhin, A few classes of periodic continued fractions, Utilitas Math. 30 (1986), 79-107. Zbl0615.10014
  10. [10] R. A. Mollin and H. C. Williams, Consecutive powers in continued fractions, Acta Arith. 61 (1992), 233-264. Zbl0764.11010
  11. [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. Zbl0766.11003
  12. [12] A. Schinzel, On some problems of the arithmetical theory of continued fractions, Acta Arith. 6 (1961), 393-413. Zbl0099.04003
  13. [13] D. Shanks, On Gauss's class number problems, Math. Comp. 23 (1969), 151-163. Zbl0177.07103
  14. [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. Zbl0223.12006
  15. [15] H. C. Williams, A note on the period length of the continued fraction expansion of certain √D, Utilitas Math. 28 (1985), 201-209. Zbl0586.10004
  16. [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. Zbl0617.10005
  17. [17] Y. Yamamoto, Real quadratic fields with large fundamental units, Osaka J. Math. 8 (1971), 261-270. Zbl0243.12001

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