Number of imaginary fields with a given class number

The class number formula shows that h(-D) is roughly \sqrt D L(1, \chi). Thus studying the distribution of class numbers can be related to the distribution of L(1, \chi_{-D}) as D varies.

https://arxiv.org/pdf/0707.0237.pdf – Soundararajan

The average value of the class number

\displaystyle \frac{1}{D} \sum_{k \leq D} h_{-4 k} \sim \frac{4 \pi}{21 \zeta(3)} \sqrt{D}

The distribution of the L values are governed by the statistics of a random Euler product.

https://arxiv.org/pdf/math/0206031.pdf – Granville, Soundararajan


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