The number of imaginary quadratic fields with a given class number

2007/07/02 by K. Soundararajan, Soundararajan, K.
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.0707.0237

openalex publication_date 2007/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the number \Cal F(h) of imaginary quadratic fields with class number h. We establish an asymptotic formula for the average value of \Cal F(h). We also establish a modest non-trivial upper bound for \Cal F(h) and give an application to a question of Rosen and Silverman on the odd part of the class number. Finally, we speculate on the asymptotic nature of \Cal F(h).

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