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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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, 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:	Date Event April 2020 Published 17 September 2019 Available 4 September 2019 Accepted
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
Related URLs:	Publisher

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