Geodesic
On the 16-rank of class groups of $\mathbb{Q}(\sqrt{-3p})$ for primes $p$ congruent to 1 modulo 4
Margherita Piccolo1
1 Heinrich-Heine-Universität, Düsseldorf Universitätsstr. 1 40225 Düsseldorf, Germany
Acta Arithmetica, Tome 202 (2022) no. 1, pp. 1-20

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

For fixed $q\in \{3,7,11,19, 43,67,163\}$, we consider the density of primes $p$ congruent to $1$ modulo $4$ such that the class group of the number field $\mathbb {Q}(\sqrt {-qp})$ has order divisible by $16$. We show that this density is equal to $1/8$, in line with a more general conjecture of Gerth. Vinogradov’s method is the key analytic tool for our work.
DOI : 10.4064/aa200422-9-6
Keywords: fixed consider density primes congruent modulo class group number field mathbb sqrt qp has order divisible density equal line general conjecture gerth vinogradov method key analytic tool work

Margherita Piccolo 1

1 Heinrich-Heine-Universität, Düsseldorf Universitätsstr. 1 40225 Düsseldorf, Germany 
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Margherita Piccolo. On the 16-rank of class groups of $\mathbb{Q}(\sqrt{-3p})$ for primes $p$ congruent to 1 modulo 4. Acta Arithmetica, Tome 202 (2022) no. 1, pp. 1-20. doi: 10.4064/aa200422-9-6

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