Consecutive powers in continued fractions

• Autorzy: R. A. Mollin , H. C. Williams
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1992
• Tom: 61
• Numer: 3
• Strony: 233-264

Daty

wydano

1992

otrzymano

1990-09-07

poprawiono

1991-10-24

Twórcy

autor

R. A. Mollin

• Department of Mathematics & Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada

autor

H. C. Williams

• Department of Computer Science, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada

Bibliografia

• [1] L. Bernstein, Fundamental units and cycles, J. Number Theory 8 (1976), 446-491.
• [2] L. Bernstein, Fundamental units and cycles in the period of real quadratic number fields, Part II, Pacific J. Math. 63 (1976), 63-78.
• [3] G. Chrystal, Textbook of Algebra, part 2, 2nd ed., Dover Reprints, N.Y., 1969, 423-490.
• [4] M. D. Hendy, Applications of a continued fraction algorithm to some class number problems, Math. Comp. 28 (1974), 267-277.
• [5] C. Levesque, Continued fraction expansions and fundamental units, J. Math. Phys. Sci. 22 (1988), 11-44.
• [6] C. Levesque and G. Rhin, A few classes of periodic continued fractions, Utilitas Math. 30 (1986), 79-107.
• [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.
• [8] R. A. Mollin, Powers in continued fractions and class numbers of real quadratic fields, Utilitas Math., to appear.
• [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.
• [10] O. Perron, Die Lehre von den Kettenbrüchen, Teubner, Stuttgart 1977.
• [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] H. C. Williams, A note on the period length of the continued fraction expansion of certain √D, Utilitas Math. 28 (1985), 201-209.
• [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.