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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the divisibility of the class number of imaginary quadratic number fields


Author: Stéphane R. Louboutin
Journal: Proc. Amer. Math. Soc. 137 (2009), 4025-4028
MSC (2000): Primary 11R29; Secondary 11R11
Published electronically: July 22, 2009
MathSciNet review: 2538563
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Abstract: We prove that if at least one of the prime divisors of an odd integer $ U\geq 3$ is equal to $ 3$ mod $ 4$, then the ideal class group of the imaginary quadratic field $ \mathbf{Q}(\sqrt{1-4U^n})$ contains an element of order $ n$.


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Additional Information

Stéphane R. Louboutin
Affiliation: Institut de Mathématiques de Luminy, UMR 6206, 163, avenue de Luminy, Case 907, 13288 Marseille Cedex 9, France
Email: loubouti@iml.univ-mrs.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10021-7
PII: S 0002-9939(09)10021-7
Keywords: Class number, imaginary quadratic field, divisibility
Received by editor(s): March 20, 2009
Received by editor(s) in revised form: April 9, 2009
Published electronically: July 22, 2009
Communicated by: Ken Ono
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.