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.

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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:	Date Event 8 February 2022 Published 15 April 2021 Accepted
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

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