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Mathematics of Computation

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Ambiguous classes in quadratic fields


Author: R. A. Mollin
Journal: Math. Comp. 61 (1993), 355-360
MSC: Primary 11R29; Secondary 11R09, 11R11
MathSciNet review: 1195434
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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 [Enhancements On Off] (What's this?)

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  • [2] 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, 10.4153/CJM-1992-049-0
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  • [5] 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

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1993-1195434-9
Keywords: Ambiguous ideal, quadratic field, class number, exponent
Article copyright: © Copyright 1993 American Mathematical Society