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2020 The distribution of $p$-torsion in degree $p$ cyclic fields
Jack Klys
Algebra Number Theory 14(4): 815-854 (2020). DOI: 10.2140/ant.2020.14.815

Abstract

We compute all the moments of the p-torsion in the first step of a filtration of the class group defined by Gerth (1987) for cyclic fields of degree p, unconditionally for p=3 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 p=3 case this gives the distribution of the 3-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 4-torsion in quadratic fields.

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Jack Klys. "The distribution of $p$-torsion in degree $p$ cyclic fields." Algebra Number Theory 14 (4) 815 - 854, 2020. https://doi.org/10.2140/ant.2020.14.815

Information

Received: 30 June 2017; Revised: 30 October 2019; Accepted: 27 November 2019; Published: 2020
First available in Project Euclid: 30 June 2020

zbMATH: 07224491
MathSciNet: MR4114057
Digital Object Identifier: 10.2140/ant.2020.14.815

Subjects:
Primary: 11R29
Secondary: 11R37, 11R45

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.14 • No. 4 • 2020
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