Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

The unit equation over cyclic number fields of prime degree

Tools
- Tools
+ Tools

Freitas, Nuno, Kraus, Alain and Siksek, Samir (2022) The unit equation over cyclic number fields of prime degree. Algebra & Number Theory, 15 (10). pp. 2647-2653. doi:10.2140/ant.2021.15.2647 ISSN 1937-0652.

[img]
Preview
PDF
WRAP-unit-equation-over-cyclic-number-fields-prime-degree-2022.pdf - Published Version - Requires a PDF viewer.

Download (1346Kb) | Preview
[img] PDF
WRAP-unit-equation-over-cyclic-number-fields-prime-degree-Siksek-2021.pdf - Accepted Version
Embargoed item. Restricted access to Repository staff only - Requires a PDF viewer.

Download (482Kb)
Official URL: https://doi.org/10.2140/ant.2021.15.2647

Request Changes to record.

Abstract

Let ℓ≠3 be a prime. We show that there are only finitely many cyclic number fields F of degree ℓ for which the unit equation λ+μ=1, λ,μ∈O×F has solutions. Our result is effective. For example, we deduce that the only cyclic quintic number field for which the unit equation has solutions is Q(ζ11)+.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Cyclic permutations, Algebraic fields
Journal or Publication Title: Algebra & Number Theory
Publisher: Mathematical Sciences Publishers
ISSN: 1937-0652
Official Date: 8 February 2022
Dates:
DateEvent
8 February 2022Published
15 April 2021Accepted
Volume: 15
Number: 10
Page Range: pp. 2647-2653
DOI: 10.2140/ant.2021.15.2647
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 21 April 2021
Date of first compliant Open Access: 18 February 2022
Related URLs:
  • Publisher

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics

twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us