Statistics of k-groups modulo p for the ring of integers of a varying quadratic number field

Bruce W. Jordan; Zev Klagsbrun; Bjorn Poonen; Christopher Skinner; Yevgeny Zaytman

doi:10.2140/tunis.2020.2.287

Statistics of k-groups modulo p for the ring of integers of a varying quadratic number field

Bruce W. Jordan, Zev Klagsbrun, Bjorn Poonen, Christopher Skinner, Yevgeny Zaytman

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

For each odd prime p, we conjecture the distribution of the p-torsion subgroup of K_2n (O_F) as F ranges over real quadratic fields, or over imaginary quadratic fields. We then prove that the average size of the 3-torsion subgroup of K_2n (O_F) is as predicted by this conjecture.

Original language	English (US)
Pages (from-to)	287-307
Number of pages	21
Journal	Tunisian Journal of Mathematics
Volume	2
Issue number	2
DOIs	https://doi.org/10.2140/tunis.2020.2.287
State	Published - 2020

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Algebraic K-theory
Class group
Cohen-Lenstra heuristics
Ring of integers

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10.2140/tunis.2020.2.287

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abstract = "For each odd prime p, we conjecture the distribution of the p-torsion subgroup of K2n (OF) as F ranges over real quadratic fields, or over imaginary quadratic fields. We then prove that the average size of the 3-torsion subgroup of K2n (OF) is as predicted by this conjecture.",

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AU - Jordan, Bruce W.

AU - Klagsbrun, Zev

AU - Poonen, Bjorn

AU - Skinner, Christopher

AU - Zaytman, Yevgeny

PY - 2020

Y1 - 2020

N2 - For each odd prime p, we conjecture the distribution of the p-torsion subgroup of K2n (OF) as F ranges over real quadratic fields, or over imaginary quadratic fields. We then prove that the average size of the 3-torsion subgroup of K2n (OF) is as predicted by this conjecture.

AB - For each odd prime p, we conjecture the distribution of the p-torsion subgroup of K2n (OF) as F ranges over real quadratic fields, or over imaginary quadratic fields. We then prove that the average size of the 3-torsion subgroup of K2n (OF) is as predicted by this conjecture.

KW - Algebraic K-theory

KW - Class group

KW - Cohen-Lenstra heuristics

KW - Ring of integers

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JO - Tunisian Journal of Mathematics

JF - Tunisian Journal of Mathematics

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ER -

Statistics of k-groups modulo p for the ring of integers of a varying quadratic number field

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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