Consecutive powers in continued fractions

R. A. Mollin; H. C. Williams

Acta Arithmetica (1992)

  • Volume: 61, Issue: 3, page 233-264
  • ISSN: 0065-1036

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R. A. Mollin, and H. C. Williams. "Consecutive powers in continued fractions." Acta Arithmetica 61.3 (1992): 233-264. <http://eudml.org/doc/206464>.

@article{R1992,
author = {R. A. Mollin, H. C. Williams},
journal = {Acta Arithmetica},
keywords = {reduced ideals; upper bound; regulator; continued fraction expansion; period length},
language = {eng},
number = {3},
pages = {233-264},
title = {Consecutive powers in continued fractions},
url = {http://eudml.org/doc/206464},
volume = {61},
year = {1992},
}

TY - JOUR
AU - R. A. Mollin
AU - H. C. Williams
TI - Consecutive powers in continued fractions
JO - Acta Arithmetica
PY - 1992
VL - 61
IS - 3
SP - 233
EP - 264
LA - eng
KW - reduced ideals; upper bound; regulator; continued fraction expansion; period length
UR - http://eudml.org/doc/206464
ER -

References

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  1. [1] L. Bernstein, Fundamental units and cycles, J. Number Theory 8 (1976), 446-491. Zbl0352.10002
  2. [2] L. Bernstein, Fundamental units and cycles in the period of real quadratic number fields, Part II, Pacific J. Math. 63 (1976), 63-78. Zbl0335.10011
  3. [3] G. Chrystal, Textbook of Algebra, part 2, 2nd ed., Dover Reprints, N.Y., 1969, 423-490. 
  4. [4] M. D. Hendy, Applications of a continued fraction algorithm to some class number problems, Math. Comp. 28 (1974), 267-277. Zbl0275.12007
  5. [5] C. Levesque, Continued fraction expansions and fundamental units, J. Math. Phys. Sci. 22 (1988), 11-44. Zbl0645.10010
  6. [6] C. Levesque and G. Rhin, A few classes of periodic continued fractions, Utilitas Math. 30 (1986), 79-107. Zbl0615.10014
  7. [7] R. A. Mollin, Prime powers in continued fractions related to the class number one problem for real quadratic fields, C. R. Math. Rep. Acad. Sci. Canada 11 (1989), 209-213. Zbl0705.11061
  8. [8] R. A. Mollin, Powers in continued fractions and class numbers of real quadratic fields, Utilitas Math., to appear. Zbl0776.11002
  9. [9] R. A. Mollin and H. C. Williams, Powers of 2, continued fractions and the class number one problem for real quadratic fields ℚ(√d) with d ≡ 1 (mod 8), in: The Mathematical Heritage of C. F. Gauss, G. M. Rassias (ed.), World Sci., 1991, 505-516. Zbl0771.11006
  10. [10] O. Perron, Die Lehre von den Kettenbrüchen, Teubner, Stuttgart 1977. Zbl43.0283.04
  11. [11] D. Shanks, The infrastructure of a real quadratic field and its applications, in: Proc. 1972 Number Theory Conf., Univ. of Colorado, Boulder, Colo., 1973, 217-224. 
  12. [12] 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
  13. [13] H. C. Williams and M. C. Wunderlich, On the parallel generation of the residues for the continued fraction factoring algorithm, Math. Comp. 177(1987), 405-423. Zbl0617.10005

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