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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
Posted:
July 22, 2009
MathSciNet review:
2538563
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Additional Information
Abstract: We prove that if at least one of the prime divisors of an odd integer  is equal to  mod  , then the ideal class group of the imaginary quadratic field  contains an element of order  .
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(1997), no. 3-4, 267–283. Computational algebra and number
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Soundararajan, Divisibility of class numbers of imaginary quadratic
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no. 3, 681–690. MR 1766097
(2001i:11128), http://dx.doi.org/10.1112/S0024610700008887
- [AC]
- N. C. Ankeny and S. Chowla, On the divisibility of the class number of quadratic fields, Pacific J. Math. 5 (1955), 321-324. MR 0085301 (19:18f)
- [BH]
- Y. Bilu and G. Hanrot, Solving Thue equations of high degree, J. Number Theory 60 (1996), 373-392. MR 1412969 (97k:11040)
- [Co]
- J. H. E. Cohn, On the class number of certain imaginary quadratic fields, Proc. Amer. Math. Soc. 130 (2002), 1275-1277. MR 1879947 (2002j:11127)
- [DFKPRW]
- M. Daberkow, C. Fieker, J. Klüners, M. Pohst, K. Roegner, M. Schörnig and K. Wildanger, KANT V4, J. Symbolic Comput. 24 (1997), 267-283. MR 1484479 (99g:11150)
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- B. H. Gross and D. E. Rohrlich, Some results on the Mordell-Weil group of the Jacobian of the Fermat curve, Inventiones Math. 44 (1978), 201-224. MR 0491708 (58:10911)
- [Ki]
- Y. Kishi, Note on the divisibility of the class number of certain imaginary quadratic fields, Glasgow Math. J. 51 (2009), 187-191. MR 2471686
- [Mur]
- M. Ram Murty, Exponents of class groups of quadratic fields, Topics in number theory (University Park, PA, 1997), 229-239, Math. Appl., 467, Kluwer Acad. Publ., Dordrecht, 1999. MR 1691322 (2000b:11123)
- [So]
- K. Soundararajan, Divisibility of class numbers of imaginary quadratic fields, J. London Math. Soc. (2) 61 (2000), 681-690. MR 1766097 (2001i:11128)
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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
Posted:
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.
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