Ambiguous classes in quadratic fields
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- by R. A. Mollin PDF
- Math. Comp. 61 (1993), 355-360 Request permission
Abstract:
We provide sufficient conditions for the class group of a quadratic field (with positive or negative discriminant) to be generated by ambiguous ideals. This investigation was motivated by a recent result of F. Halter-Koch, which we show is false.References
- F. Halter-Koch, Prime-producing quadratic polynomials and class numbers of quadratic orders, Computational number theory (Debrecen, 1989) de Gruyter, Berlin, 1991, pp. 73–82. MR 1151856
- S. Louboutin, R. A. Mollin, and H. C. Williams, Class numbers of real quadratic fields, continued fractions, reduced ideals, prime-producing quadratic polynomials and quadratic residue covers, Canad. J. Math. 44 (1992), no. 4, 824–842. MR 1178571, DOI 10.4153/CJM-1992-049-0
- R. A. Mollin and H. C. Williams, Prime producing quadratic polynomials and real quadratic fields of class number one, Théorie des nombres (Quebec, PQ, 1987) de Gruyter, Berlin, 1989, pp. 654–663. MR 1024594
- R. A. Mollin and H. C. Williams, On prime valued polynomials and class numbers of real quadratic fields, Nagoya Math. J. 112 (1988), 143–151. MR 974269, DOI 10.1017/S0027763000001185
- R. A. Mollin and H. C. Williams, Solution of the class number one problem for real quadratic fields of extended Richaud-Degert type (with one possible exception), Number theory (Banff, AB, 1988) de Gruyter, Berlin, 1990, pp. 417–425. MR 1106676
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Math. Comp. 61 (1993), 355-360
- MSC: Primary 11R29; Secondary 11R09, 11R11
- DOI: https://doi.org/10.1090/S0025-5718-1993-1195434-9
- MathSciNet review: 1195434