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

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.