Imaginary quadratic fields with class groups of 3-rank at least 2

Abstract

In this short note, we construct a family of imaginary quadratic fields whose class group has 3-rank at least 2. We show that, for every large X, there are \(\gg X^{\frac{1}{2}-\epsilon }\) such fields with the discriminant \(-D\) satisfying \(D\le X\).

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Acknowledgements

We thank Professor Michael Filaseta for helpful discussions. We are grateful to the anonymous referee for carefully reviewing this paper, correcting several issues, and suggesting some changes that improved the presentation of this work. We also thank the referee for bringing the preprint [11] to our attention.

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Correspondence to Gang Yu.

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Yu, G. Imaginary quadratic fields with class groups of 3-rank at least 2. manuscripta math. 163, 569–574 (2020). https://doi.org/10.1007/s00229-019-01172-3

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Mathematics Subject Classification

  • 11R11
  • 11R29