Heuristics for class numbers and lambda invariants

Kraft, James; Washington, Lawrence

doi:10.1090/S0025-5718-06-01921-1

Heuristics for class numbers and lambda invariants
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by James S. Kraft and Lawrence C. Washington PDF

Math. Comp. 76 (2007), 1005-1023 Request permission

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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