The number of imaginary quadratic fields with a given class number

Details The number of imaginary quadratic fields with a given class number The number of imaginary quadratic fields with a given class number

2007-07-02

arxiv.org/abs/0707.0237v2

Mathematics

Number Theory

6 pages; Version 2 has some light changes

Scientific paper

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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