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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Heuristics for class numbers and lambda invariants


Authors: James S. Kraft and Lawrence C. Washington
Journal: Math. Comp. 76 (2007), 1005-1023
MSC (2000): Primary 11R23, 11R29, 11R11
Published electronically: October 30, 2006
MathSciNet review: 2291847
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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.


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Additional 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

DOI: http://dx.doi.org/10.1090/S0025-5718-06-01921-1
PII: S 0025-5718(06)01921-1
Received by editor(s): August 23, 2005
Received by editor(s) in revised form: January 6, 2006
Published electronically: October 30, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.