Heuristics for class numbers and lambda invariants
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- by James S. Kraft and Lawrence C. Washington;
- Math. Comp. 76 (2007), 1005-1023
- DOI: https://doi.org/10.1090/S0025-5718-06-01921-1
- Published electronically: October 30, 2006
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Abstract:
Let $K=\mathbf Q(\sqrt {-d})$ be an imaginary quadratic field and let $\mathbb Q(\sqrt {3d})$ be the associated real quadratic field. Starting from the Cohen-Lenstra heuristics and Scholz’s theorem, we make predictions for the behaviors of the 3-parts of the class groups of these two fields as $d$ varies. We deduce heuristic predictions for the behavior of the Iwasawa $\lambda$-invariant for the cyclotomic $\mathbf Z_3$-extension of $K$ and test them computationally.References
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Bibliographic Information
- James S. Kraft
- Affiliation: The Ingenuity Project, Baltimore Polytechnic Institute, 1400 W. Cold Spring Lane, Baltimore, Maryland 21209
- Email: jkraft31@comcast.net
- Lawrence C. Washington
- Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
- Email: lcw@math.umd.edu
- Received by editor(s): August 23, 2005
- Received by editor(s) in revised form: January 6, 2006
- Published electronically: October 30, 2006
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 76 (2007), 1005-1023
- MSC (2000): Primary 11R23, 11R29, 11R11
- DOI: https://doi.org/10.1090/S0025-5718-06-01921-1
- MathSciNet review: 2291847