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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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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

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