# The number of imaginary quadratic fields with prime discriminant and class number up to $H$

## TL;DR

This paper derives an asymptotic formula for counting imaginary quadratic fields with prime discriminant and bounded class number, removing the need for the Generalized Riemann Hypothesis assumption.

## Contribution

It provides the first unconditional asymptotic estimate for the number of such fields as the class number bound grows.

## Key findings

- Asymptotic formula established for prime discriminant fields
- Results hold unconditionally, without GRH assumption
- Advances understanding of distribution of quadratic fields

## Abstract

In this paper, we obtain an asymptotic formula for the number of imaginary quadratic fields with prime discriminant and class number up to $H$, as $H\to \infty$. Previously, such an asymptotic was only known under the assumption of the Generalized Riemann Hypothesis, by the recent work of Holmin, Jones, Kurlberg, McLeman and Petersen.