Bounds for the ℓ‐torsion in class groups. / Widmer, Martin.

In: Bulletin of the London Mathematical Society, Vol. 50, No. 1, 02.2018, p. 124-131.

Research output: Contribution to journalArticlepeer-review

Published

Standard

Bounds for the ℓ‐torsion in class groups. / Widmer, Martin.

In: Bulletin of the London Mathematical Society, Vol. 50, No. 1, 02.2018, p. 124-131.

Research output: Contribution to journalArticlepeer-review

Harvard

Widmer, M 2018, 'Bounds for the ℓ‐torsion in class groups', Bulletin of the London Mathematical Society, vol. 50, no. 1, pp. 124-131. https://doi.org/10.1112/blms.12113

APA

Widmer, M. (2018). Bounds for the ℓ‐torsion in class groups. Bulletin of the London Mathematical Society, 50(1), 124-131. https://doi.org/10.1112/blms.12113

Vancouver

Widmer M. Bounds for the ℓ‐torsion in class groups. Bulletin of the London Mathematical Society. 2018 Feb;50(1):124-131. https://doi.org/10.1112/blms.12113

Author

Widmer, Martin. / Bounds for the ℓ‐torsion in class groups. In: Bulletin of the London Mathematical Society. 2018 ; Vol. 50, No. 1. pp. 124-131.

BibTeX

@article{7047b3e63198482aa6a3b02760b77d2b,
title = "Bounds for the ℓ‐torsion in class groups",
abstract = "We prove for each integer ℓ⩾1 an unconditional upper bound for the size of the ℓ-torsion subgroup ClK[ℓ] of the class group of K, which holds for all but a zero density set of number fields K of degree d∈{4,5} (with the additional restriction in the case d=4 that the field be non-D4). For sufficiently large ℓ this improves recent results of Ellenberg, Matchett Wood and Pierce, and is also stronger than the best currently known pointwise bounds under GRH. Conditional on GRH and on a weak conjecture on the distribution of number fields our bounds also hold for arbitrary degrees d.",
author = "Martin Widmer",
year = "2018",
month = feb,
doi = "10.1112/blms.12113",
language = "English",
volume = "50",
pages = "124--131",
journal = "Bulletin of the London Mathematical Society",
issn = "0024-6093",
publisher = "Oxford University Press",
number = "1",

}

RIS

TY - JOUR

T1 - Bounds for the ℓ‐torsion in class groups

AU - Widmer, Martin

PY - 2018/2

Y1 - 2018/2

N2 - We prove for each integer ℓ⩾1 an unconditional upper bound for the size of the ℓ-torsion subgroup ClK[ℓ] of the class group of K, which holds for all but a zero density set of number fields K of degree d∈{4,5} (with the additional restriction in the case d=4 that the field be non-D4). For sufficiently large ℓ this improves recent results of Ellenberg, Matchett Wood and Pierce, and is also stronger than the best currently known pointwise bounds under GRH. Conditional on GRH and on a weak conjecture on the distribution of number fields our bounds also hold for arbitrary degrees d.

AB - We prove for each integer ℓ⩾1 an unconditional upper bound for the size of the ℓ-torsion subgroup ClK[ℓ] of the class group of K, which holds for all but a zero density set of number fields K of degree d∈{4,5} (with the additional restriction in the case d=4 that the field be non-D4). For sufficiently large ℓ this improves recent results of Ellenberg, Matchett Wood and Pierce, and is also stronger than the best currently known pointwise bounds under GRH. Conditional on GRH and on a weak conjecture on the distribution of number fields our bounds also hold for arbitrary degrees d.

U2 - 10.1112/blms.12113

DO - 10.1112/blms.12113

M3 - Article

VL - 50

SP - 124

EP - 131

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

IS - 1

ER -