The class number formula shows that is roughly Thus studying the distribution of class numbers can be related to the distribution of as varies.
https://arxiv.org/pdf/0707.0237.pdf – Soundararajan
The average value of the class number
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