Vol. 314, No. 2, 2021

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The unit signature rank deficiency is unbounded over cyclotomic fields

David S. Dummit and Hershy Kisilevsky

Vol. 314 (2021), No. 2, 259–267
Abstract

We prove that the rank of the elementary abelian 2-group of totally positive units modulo the squares of all units in totally real cyclotomic fields can be arbitrarily large.

Keywords
cyclotomic fields, unit signature rank
Mathematical Subject Classification
Primary: 11R27
Secondary: 11R16, 11R18, 11R29, 11R80
Milestones
Received: 29 September 2020
Revised: 3 September 2021
Accepted: 6 September 2021
Published: 10 November 2021
Authors
David S. Dummit
Department of Mathematics
University of Vermont
Burlington, VT
United States
Hershy Kisilevsky
Department of Mathematics and Statistics and CICMA
Concordia University
Montréal, Quebec
Canada