The 16-rank of ℚ()

Koymans, Peter

doi:10.2140/ant.2020.14.37

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The 16-rank of $\mathbb{Q}(\sqrt{-p})$

Peter Koymans

Vol. 14 (2020), No. 1, 37–65

DOI: 10.2140/ant.2020.14.37

Abstract

Recently, a density result for the $16$ -rank of $Cl (ℚ (\sqrt{- p}))$ was established when $p$ varies among the prime numbers, assuming a short character sum conjecture. We prove the same density result unconditionally.

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Keywords

arithmetic statistics, class groups

Mathematical Subject Classification 2010

Primary: 11R29

Secondary: 11N45, 11R45

Milestones

Received: 19 September 2018

Revised: 14 August 2019

Accepted: 12 September 2019

Published: 15 March 2020

Authors

Peter Koymans
Mathematisch Instituut Leiden University Leiden Netherlands

Vol. 14, No. 1, 2020