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Fermat's last theorem and modular curves over real quadratic fields
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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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Official URL: https://doi.org/10.4064/aa210812-2-4
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 | ||||||||
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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'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: |
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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: |
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