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arXiv · 2208.06862

A note on the distribution of Iwasawa invariants of imaginary quadratic fields

Anwesh Ray
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Abstract

Given an odd prime number $p$ and an imaginary quadratic field $K$, we establish a relationship between the $p$-rank of the class group of $K$, and the classical $\lambda$-invariant of the cyclotomic $\mathbb{Z}_p$-extension of $K$. Exploiting this relationship, we prove statistical results for the distribution of $\lambda$-invariants for imaginary quadratic fields ordered according to their discriminant. Some of our results are conditional since they rely on the original Cohen--Lenstra heuristics for the distribution of the $p$-parts of class groups of imaginary quadratic fields. Some results are unconditional results ad are obtained by leveraging theorems of Byeon, Craig and others.

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Anwesh Ray. 2022-08-14. A note on the distribution of Iwasawa invariants of imaginary quadratic fields. https://doi.org/10.1007/s00574-023-00353-9

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