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September 5, 2025Open Access

Greenberg's conjecture for real quadratic number fields

Key Points

Orders of 3-class groups remain bounded as n approaches infinity, confirming Greenberg's conjecture.
Fields examined include real quadratic number fields with discriminants less than 100,000.
All computations align with predicted outcomes based on existing mathematical conjectures.
Results support the theory of cyclotomic Z_3-extensions in relation to 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. (Sat,) studied this question.

synapsesocial.com/papers/68bb46bd6d6d5674bccfea1d — DOI: https://doi.org/10.56994/jxm.001.002.001

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