Michaud-Jacobs, Philippe (2022) Fermat's last theorem and modular curves over real quadratic fields. Acta Arithmetica, 203 (4). pp. 319-351. doi:10.4064/aa210812-2-4 ISSN 0065-1036.

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Abstract

We study the Fermat equation xn+yn=zn over quadratic fields Q(d√) for squarefree d with 26≤d≤97. By studying quadratic points on the modular curves X0(N), d-regular primes, and working with Hecke operators on spaces of Hilbert newforms, we extend work of Freitas and Siksek to show that for most squarefree d in this range there are no non-trivial solutions to this equation for n≥4.

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's last theorem, Modular curves, Quadratic fields, Hecke operators, Characteristic functions
Journal or Publication Title:	Acta Arithmetica
Publisher:	Instytut Matematyczny
ISSN:	0065-1036
Official Date:	2022
Dates:	Date Event 2022 Published 9 May 2022 Available 2 April 2022 Accepted
Volume:	203
Number:	4
Page Range:	pp. 319-351
DOI:	10.4064/aa210812-2-4
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	22 April 2022
Date of first compliant Open Access:	9 May 2022
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID Studentship [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266
Related URLs:	Publisher
Open Access Version:	ArXiv

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