Ambiguous classes in quadratic fields

Author:
R. A. Mollin

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

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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 (A. Pethö, M. Pohst, H. C. Williams, and H. Zimmer, eds.), de Gruyter, Berlin, 1991, pp. 73-82. MR**1151856 (93c:11101)****[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), 1-19. MR**1178571 (93h:11117)****[3]**R. A. Mollin and H. C. Williams,*Prime producing quadratic polynomials and real quadratic fields of class number one*, Number Theory (J. M. De Koninck and C. Levesque, eds.), de Gruyter, Berlin, 1989, pp 654-663. MR**1024594 (90m:11153)****[4]**-,*On prime valued polynomials and class numbers of real quadratic fields*, Nagoya Math. J.**112**(1988), 143-151. MR**974269 (90c:11080)****[5]**-,*Solution of the class number one problem for real quadratic fields of extended Richaud-Degert type*(*with one possible exception*), Number Theory (R. A. Mollin, ed.), de Gruyter, Berlin, 1990, pp. 417-425. MR**1106676 (92f:11144)**

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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