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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

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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
Subjects: Q Science > QA Mathematics
Divisions: Faculty of 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:
DateEvent
April 2020Published
17 September 2019Available
4 September 2019Accepted
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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