On the divisibility of the class number of imaginary quadratic number fields
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- by Stéphane R. Louboutin PDF
- Proc. Amer. Math. Soc. 137 (2009), 4025-4028 Request permission
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 $n$.References
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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
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 4025-4028
- MSC (2000): Primary 11R29; Secondary 11R11
- DOI: https://doi.org/10.1090/S0002-9939-09-10021-7
- MathSciNet review: 2538563