Algebra & Number Theory
- Algebra Number Theory
- Volume 14, Number 4 (2020), 815-854.
The distribution of $p$-torsion in degree $p$ cyclic fields
We compute all the moments of the -torsion in the first step of a filtration of the class group defined by Gerth (1987) for cyclic fields of degree , unconditionally for and under GRH in general. We show that it satisfies a distribution which Gerth conjectured as an extension of the Cohen–Lenstra–Martinet conjectures. In the case this gives the distribution of the -torsion of the class group modulo the Galois invariant part. We follow the strategy used by Fouvry and Klüners (2007) in their proof of the distribution of the -torsion in quadratic fields.
Algebra Number Theory, Volume 14, Number 4 (2020), 815-854.
Received: 30 June 2017
Revised: 30 October 2019
Accepted: 27 November 2019
First available in Project Euclid: 30 June 2020
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Klys, Jack. The distribution of $p$-torsion in degree $p$ cyclic fields. Algebra Number Theory 14 (2020), no. 4, 815--854. doi:10.2140/ant.2020.14.815. https://projecteuclid.org/euclid.ant/1593482419