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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
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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 | ||||||||
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