Imaginary quadratic number fields with class groups of small exponent

Andreas-Stephan Elsenhans; Jürgen Klüners; Florin Nicolae

Imaginary quadratic number fields with class groups of small exponent

Number Theory 2018-03-07 v1

Authors: Andreas-Stephan Elsenhans , Jürgen Klüners , Florin Nicolae

Abstract

Let $D<0$ be a fundamental discriminant and denote by $E(D)$ the exponent of the ideal class group $\text{Cl}(D)$ of $K={\mathbb Q}(\sqrt{D})$ . Under the assumption that no Siegel zeros exist we compute all such $D$ with $E(D)$ is a divisor of $8$ . We compute all $D$ with $|D|\leq 3.1\cdot 10^{20}$ such that $E(D)\leq 8$ .

Keywords

class number of quadratic fields quadratic forms

Cite

@article{arxiv.1803.02056,
  title  = {Imaginary quadratic number fields with class groups of small exponent},
  author = {Andreas-Stephan Elsenhans and Jürgen Klüners and Florin Nicolae},
  journal= {arXiv preprint arXiv:1803.02056},
  year   = {2018}
}

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