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October 13, 2025Open Access

Greenberg's conjecture for real quadratic number fields

Key Points

The orders of the 3-class groups remain bounded as n increases, consistent with Greenberg's conjecture.
This research computes the 3-class groups for real quadratic fields with discriminants less than 100,000.
The analysis focuses on the cyclotomic extensions of the real quadratic fields.
Findings support the conjecture's validity, providing insights into the structure of these number fields.

Abstract

We compute the 3-class groups Aₙ of the fields Fₙ in the cyclotomic Z₃-extensions of the real quadratic fields of discriminant f<100, 000. In all cases the orders of Aₙ remain bounded as n goes to infinity. This is in agreement with Greenberg's conjecture.

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Mercuri et al. (Sun,) studied this question.

synapsesocial.com/papers/68ecc715d1cc7436f7d18bcf — DOI: https://doi.org/10.48550/arxiv.2503.00819

Authors

Pietro Mercuri

University of Rome Tor Vergata

Maurizio Paoluzi

René Schoof

University of Rome Tor Vergata

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Greenberg's conjecture for real quadratic number fields

Key Points

Abstract

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Discussion

Cite this study

Authors

Actions

References and Citations

Citation Network

Connected Papers

Discussion

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