On real quadratic fields of class number two
Authors:
R. A. Mollin and H. C. Williams
Journal:
Math. Comp. 59 (1992), 625632
MSC:
Primary 11R11; Secondary 11R29
MathSciNet review:
1136224
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Abstract: It is the primary purpose of the paper to determine all real quadratic fields of class number when (with one possible exception). Here, k is the period length of the continued fraction expansion of either , in the case or 3 , or of , in the case .
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, Computation of the class numbers of a real quadratic field, Advances in the Theory of Computing and Comput. Math. (to appear).
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quadratic fields of extended RichaudDegert type (with one possible
exception), Number theory (Banff, AB, 1988) de Gruyter, Berlin,
1990, pp. 417–425. MR 1106676
(92f:11144)
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C. Williams, On a determination of real quadratic fields of class
number one and related continued fraction period length less than 25,
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20–25. MR
1103974 (92c:11113)
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(1991), no. 5, 139–144. MR 1114957
(92h:11091)
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C. Williams and M.
C. Wunderlich, On the parallel generation of the
residues for the continued fraction factoring algorithm, Math. Comp. 48 (1987), no. 177, 405–423. MR 866124
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 [1]
 R. A. Mollin and H. C. Williams, On a solution of a class number two problem for a family of real quadratic fields, Computational Number Theory (A. Pethö, M. Pohst, H. Williams, and H. Zimmer, eds.), Walter de Gruyter, Berlin, 1991, pp. 95101. MR 1151858 (93d:11118)
 [2]
 , Computation of the class numbers of a real quadratic field, Advances in the Theory of Computing and Comput. Math. (to appear).
 [3]
 R. A. Mollin and H. C. Williams, Primeproducing quadratic polynomials and real quadratic fields of class number one, Number Theory (J. M. DeKoninck and C. Levesque, eds.), Walter de Gruyter, Berlin, 1989, pp. 654663. MR 1024594 (90m:11153)
 [4]
 , Class number one for real quadratic fields, continued fractions and reduced ideals, Number Theory and Applications (R. A. Mollin, ed.), Kluwer, Dordrecht, 1989, pp. 481496. MR 1123091 (92f:11143)
 [5]
 , Solution of the class number one problem for real quadratic fields of extended RichaudDegert type (with one possible exception), Number Theory (R. A. Mollin, ed.), Walter de Gruyter, Berlin, 1990, pp. 417425. MR 1106676 (92f:11144)
 [6]
 , On a determination of real quadratic fields of class number one and related continued fraction period length less than 25, Proc. Japan Acad. Ser. A Math. Sci. 67 (1991), 2025. MR 1103974 (92c:11113)
 [7]
 A. J. Stephens and H. C. Williams, Some computational results on a problem concerning powerful numbers, Math. Comp. 50 (1988), 619632. MR 929558 (89d:11091)
 [8]
 T. Tatuzawa, On a theorem of Siegel, Japan J. Math. 21 (1951), 163178. MR 0051262 (14:452c)
 [9]
 H. Taya and N. Terai, Determination of certain real quadratic fields with class number two, Proc. Japan Acad. Ser. A Math. Sci. 67 (1991), 139144. MR 1114957 (92h:11091)
 [10]
 H. C. Williams and M. C. Wunderlich, On the parallel generation of the residues for the continued fraction factoring algorithm, Math. Comp. 48 (1987), 405423. MR 866124 (88i:11099)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718199211362241
PII:
S 00255718(1992)11362241
Keywords:
Real quadratic field,
class number,
continued fraction
Article copyright:
© Copyright 1992
American Mathematical Society
