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arXiv · 2104.08561

Conjectures on the distribution behavior of the class numbers of certain real quadratic number fields

Jinwen Xu
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Abstract

Given a random real quadratic field from $\{ \mathbb{Q}(\sqrt{p}\,) ~|~ p \text{ primes} \}$, the conjectural probability $\mathbb{P}(h=q)$ that it has class number $q$ is given for all positive odd integers $q$. Some related conjectures of the Cohen-Lenstra heuristic are given here as corollaries. These results suggest that the set of real quadratic number fields may have some natural hierarchical structures.

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Jinwen Xu. 2021-04-17. Conjectures on the distribution behavior of the class numbers of certain real quadratic number fields. https://arxiv.org/abs/2104.08561

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