What type of study is this?

September 5, 2025Open Access

Greenberg's conjecture for real quadratic number fields

View Full Paper

Ask AI

Bookmark

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.

Implication

Analysis computes 3-class groups A_n in cyclotomic Z_3-extensions, confirming Greenberg's conjecture.

Abstract

We compute the 3-class groups A_n of the fields F_n in the cyclotomic Z_3-extensions of the real quadratic fields of discriminant f < 100,000. In all cases the orders of A_n remain bounded as n goes to infinity. This is in agreement with Greenberg's conjecture.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Mercuri et al. (2025) studied this question.

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

View Full Paper

Ask AI

Bookmark

Implication

Analysis computes 3-class groups A_n in cyclotomic Z_3-extensions, confirming Greenberg's conjecture.

Greenberg's conjecture for real quadratic number fields

Key Points

Implication

Abstract

Discussion

Cite This Study

Greenberg's conjecture for real quadratic number fields

Key Points

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading