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arXiv · 1610.00226

The Distribution of p-Torsion in Degree p Cyclic Fields

Jack Klys
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Abstract

We compute all the moments of the p-torsion in the first step of a filtration of the class group defined by Gerth 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 Kluners in their proof of the distribution of the 4-torsion in quadratic fields.

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Jack Klys. 2016-12-14. The Distribution of p-Torsion in Degree p Cyclic Fields. https://doi.org/10.2140/ant.2020.14.815

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