Greenberg's conjecture for real quadratic number fields
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909520439017472 |
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| author | Mercuri, Pietro Paoluzi, Maurizio Schoof, René |
| author_facet | Mercuri, Pietro Paoluzi, Maurizio Schoof, René |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00819 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Greenberg's conjecture for real quadratic number fields Mercuri, Pietro Paoluzi, Maurizio Schoof, René Number Theory 11R23 (Primary) 11R11, 11R27, 11R29 (Secondary) 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. |
| title | Greenberg's conjecture for real quadratic number fields |
| topic | Number Theory 11R23 (Primary) 11R11, 11R27, 11R29 (Secondary) |
| url | https://arxiv.org/abs/2503.00819 |