PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Imaginary quadratic number fields with class groups of small exponent

Volume 193 / 2020

Andreas-Stephan Elsenhans, Jürgen Klüners, Florin Nicolae 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 $E(D)\leq 8$.

Authors

  • Andreas-Stephan ElsenhansUniversität Würzburg
    Campus Hubland Nord
    Emil-Fischer-Str. 30
    97074 Würzburg, Germany
    e-mail
  • Jürgen KlünersInstitut für Mathematik
    Fakultät EIM
    Universität Paderborn
    Warburger Str. 100
    33098 Paderborn, Germany
    e-mail
  • Florin Nicolae“Simion Stoilow” Institute of Mathematics
    of the Romanian Academy
    P.O. Box 1-764
    RO-014700 Bucureşti, Romania
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image