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The unit equation over cyclic number fields of prime degree
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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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Official URL: https://doi.org/10.2140/ant.2021.15.2647
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 | ||||||
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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: |
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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 | ||||||
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