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Mathematics of Computation

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Imaginary multiquadratic number fields with class group of exponent $3$ and $5$


Authors: Jürgen Klüners and Toru Komatsu
Journal: Math. Comp. 90 (2021), 1483-1497
MSC (2020): Primary 11R29; Secondary 11R11, 11R20, 11Y40
DOI: https://doi.org/10.1090/mcom/3609
Published electronically: January 26, 2021
MathSciNet review: 4232232
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Abstract: In this paper we obtain a complete list of imaginary $n$-quadratic fields with class groups of exponent $3$ and $5$ under extended Riemann hypothesis for every positive integer $n$ where an $n$-quadratic field is a number field of degree $2^n$ represented as the composite of $n$-quadratic fields.


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Additional Information

Jürgen Klüners
Affiliation: Institut für Mathematik, Universität Paderborn, Warburger Str. 100, 33098 Paderborn, Germany
ORCID: 0000-0001-6825-307X
Email: klueners@math.uni-paderborn.de

Toru Komatsu
Affiliation: Faculty of Science and Technology, Department of Mathematics, Tokyo University of Science, 2641 Yamazaki, Noda-shi, Chiba-ken 278-8510, Japan
MR Author ID: 673966
Email: komatsu@ma.noda.tus.ac.jp

Received by editor(s): May 6, 2020
Received by editor(s) in revised form: September 14, 2020
Published electronically: January 26, 2021
Additional Notes: The research was done during a sabbatical of the second author at Paderborn University.
Article copyright: © Copyright 2021 American Mathematical Society