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arXiv · 2503.00819

Greenberg's conjecture for real quadratic number fields

Pietro Mercuri·Maurizio Paoluzi·René Schoof
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Abstract

We compute the $3$-class groups $A_n$ of the fields $F_n$ in the cyclotomic $\mathbf{Z}_3$-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.

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Pietro Mercuri, Maurizio Paoluzi, René Schoof. 2025-03-02. Greenberg's conjecture for real quadratic number fields. https://arxiv.org/abs/2503.00819

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