We compute the $3$-class groups $A_n$ of the fields $F_n$ in the cyclotomic $\ZZ_3$-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.
Greenberg's conjecture for real quadratic number fields / Mercuri, Pietro; Paoluzi, Maurizio; Schoof, René. - In: THE JOURNAL OF EXPERIMENTAL MATHEMATICS. - ISSN 3069-1125. - 1:2(2025), pp. 207-217. [10.56994/jxm.001.002.001]
Greenberg's conjecture for real quadratic number fields
Mercuri, Pietro;
2025
Abstract
We compute the $3$-class groups $A_n$ of the fields $F_n$ in the cyclotomic $\ZZ_3$-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.File allegati a questo prodotto
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