On the class number of certain imaginary quadratic fields
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- by J. H. E. Cohn PDF
- Proc. Amer. Math. Soc. 130 (2002), 1275-1277 Request permission
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
- Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
- Benedict H. Gross and David E. Rohrlich, Some results on the Mordell-Weil group of the Jacobian of the Fermat curve, Invent. Math. 44 (1978), no. 3, 201–224. MR 491708, DOI 10.1007/BF01403161
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
- Received by editor(s): October 31, 2000
- Published electronically: October 5, 2001
- Communicated by: David E. Rohrlich
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1275-1277
- MSC (2000): Primary 11R29; Secondary 11D61, 11B37, 11B39
- DOI: https://doi.org/10.1090/S0002-9939-01-06255-4
- MathSciNet review: 1879947