Unramified 3-extensions over cyclic cubic fields

Akito Nomura

Vol. 230 (2007), No. 1, 167–183

DOI: 10.2140/pjm.2007.230.167

Abstract

We study the existence of unramified 3-extensions over cyclic cubic fields. As an application, we study the class number relation between certain cubic fields.

Keywords

cyclic field, cubic field, unramified extension, 3-extension, class number

Mathematical Subject Classification 2000

Primary: 12F12, 11R29

Milestones

Received: 7 August 2005

Revised: 3 November 2005

Accepted: 4 November 2005

Published: 1 March 2007