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.
Mercuri, P., Paoluzi, M., Schoof, R. (2025). Greenberg's conjecture for real quadratic number fields. THE JOURNAL OF EXPERIMENTAL MATHEMATICS, 1(2), 207-217 [10.56994/jxm.001.002.001].
Greenberg's conjecture for real quadratic number fields
Mercuri, Pietro
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2025-08-30
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.
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