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

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.

arXiv comment13 pages. Incorporated the referee's comments. To appear in QJM