Greenberg's conjecture for real quadratic number fields

Pietro Mercuri; Maurizio Paoluzi; René Schoof

Greenberg's conjecture for real quadratic number fields

Number Theory 2025-03-04 v1

Authors: Pietro Mercuri , Maurizio Paoluzi , René Schoof

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.

Keywords

class number of quadratic fields fields conjectures and proofs

Cite

@article{arxiv.2503.00819,
  title  = {Greenberg's conjecture for real quadratic number fields},
  author = {Pietro Mercuri and Maurizio Paoluzi and René Schoof},
  journal= {arXiv preprint arXiv:2503.00819},
  year   = {2025}
}

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