REVIEW 1 cited by
Monogenicity and 2-torsion in the class group of number fields of odd degree
Not yet reviewed by Pith; the record is open.
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
abstract
We study the average $2$-torsion in the class group of monogenised fields of odd degree. Bhargava--Hanke--Shankar have recently shown that for a fixed signature, the average number of non-trivial $2$-torsion elements in the class group of monogenised cubic fields is exactly twice the value predicted by the Cohen--Lenstra--Martinet--Malle heuristic over the full $S_3$ family. For any odd degree $n \ge 3$ and signature, we prove that the average number of non-trivial $2$-torsion elements in the class group of monogenised fields is at most twice the value predicted by the Cohen--Lenstra--Martinet--Malle heuristic over the full $S_n$ family. Conditional on a tail estimate for $n \ge 5$, this establishes that the doubling phenomenon discovered by Bhargava--Hanke--Shankar persists across all odd degrees and signatures.
Forward citations
Cited by 1 Pith paper
-
Geometry-of-numbers methods over global fields II: Coregular representations
Geometry-of-numbers methods are extended to count orbits in coregular spaces over arbitrary global fields, yielding bounds on average ranks and Selmer sizes for elliptic curves and hyperelliptic Jacobians.
Discussion (0). Sign in to comment.