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On Serre's modularity conjecture and Fermat's equation over quadratic imaginary fields of class number one
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Ţurcaş, George C. (2020) On Serre's modularity conjecture and Fermat's equation over quadratic imaginary fields of class number one. Journal of Number Theory, 209 . pp. 516-530. doi:10.1016/j.jnt.2019.08.011 ISSN 0022-314X.
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Official URL: https://doi.org/10.1016/j.jnt.2019.08.011
Abstract
In the present article, we extend previous results of the author and we show that when K is any quadratic imaginary field of class number one, Fermat's equation does not have integral coprime solutions such that and is prime. The results are conjectural upon the veracity of a natural generalisation of Serre's modularity conjecture.
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): | Fermat numbers, Bianchi groups, Galois theory | ||||||||
Journal or Publication Title: | Journal of Number Theory | ||||||||
Publisher: | Academic Press | ||||||||
ISSN: | 0022-314X | ||||||||
Official Date: | April 2020 | ||||||||
Dates: |
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Volume: | 209 | ||||||||
Page Range: | pp. 516-530 | ||||||||
DOI: | 10.1016/j.jnt.2019.08.011 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 12 September 2019 | ||||||||
Date of first compliant Open Access: | 17 September 2020 | ||||||||
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