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

2021/04/17 by Jinwen Xu, Xu, Jinwen
Mathematics · #11R29 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2104.08561

openalex publication_date 2021/04/17 · openalex created_date 2021/04/26 · openalex updated_date 2026/07/28

Abstract

Given a random real quadratic field from \ ℚ(√(p) ) ~|~ p primes \, the conjectural probability 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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