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 | References | Similar Articles | Additional Information

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.

**[1]**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****[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**[3]**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****[4]**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****[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