Pith. sign in

REVIEW 2 cited by

The mean number of 2-torsion elements in the class groups of $n$-monogenized cubic fields

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2010.15744 v1 pith:TYQZKLT4 submitted 2020-10-29 math.NT

Manjul Bhargava , Jonathan Hanke , Arul Shankar This is my paper
classification math.NT
keywords classcubicmonogenicitytorsionalteringaveragebehavioreffect
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We prove that, on average, the monogenicity or $n$-monogenicity of a cubic field has an altering effect on the behavior of the 2-torsion in its class group.

Discussion (0). Sign in to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A parametrization of $3$-class groups of quadratic rings over Dedekind domains

    math.NT 2025-09 conditional novelty 7.0 of 10

    Orbits of binary cubic forms under GL(R ⊕ a) are canonically in bijection with 3-torsion ideal classes of quadratic rings over any Dedekind domain R with char(R) ≠ 3, with the Steinitz class [a] as an explicit parameter.

  2. The second moment of the size of the $2$-class group of monogenized cubic fields

    math.NT 2025-06 conditional novelty 7.0 of 10

    The second moment of the size of the 2-class group of monogenized cubic fields is at most 3 for totally real fields and at most 6 for complex fields, with matching lower bounds conditional on a tail estimate.

Pith tools