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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

On the class number of certain imaginary quadratic fields

Author(s): J. H. E. Cohn
Journal: Proc. Amer. Math. Soc. 130 (2002), 1275-1277.
MSC (2000): Primary 11R29; Secondary 11D61, 11B37, 11B39
Posted: October 5, 2001
MathSciNet review: 1879947
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Abstract | References | Similar articles | Additional information

Abstract: Theorem. Let $n>2$ denote an integer, $D$ the square-free part of $2^n-1$ and $h$ the class number of the field $Q[\sqrt{-D}]$. Then except for the case $n=6$, $n-2$ divides $h$.

References:

1.
N. C. Ankeny and S. Chowla, On the divisibility of the class numbers of quadratic fields, Pacific J. Math. 5 (1955), 321-324. MR 19:18f

2.
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 58:10911

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Additional Information:

J. H. E. Cohn
Affiliation: Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom
Email: J.Cohn@rhul.ac.uk

DOI: 10.1090/S0002-9939-01-06255-4
PII: S 0002-9939(01)06255-4
Received by editor(s): October 31, 2000
Posted: October 5, 2001
Communicated by: David E. Rohrlich
Copyright of article: Copyright 2001, American Mathematical Society




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