Imaginary quadratic number fields with class groups of small exponent
Volume 193 / 2020
Acta Arithmetica 193 (2020), 217-233
MSC: Primary 11R29; Secondary 11R11.
DOI: 10.4064/aa180220-20-3
Published online: 24 January 2020
Abstract
Let $D \lt 0$ be a fundamental discriminant and denote by $E(D)$ the exponent of the ideal class group $\operatorname{Cl} (D)$ of $K=\mathbb Q (\sqrt {D})$. Under the assumption that no Siegel zeros exist we compute all such $D$ with $E(D)$ dividing $8$. We compute all $D$ with $|D|\leq 3.1\cdot 10^{20}$ such that $E(D)\leq 8$.
