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Fermat’s last theorem over some small real quadratic fields

Title data

Freitas, Nuno ; Siksek, Samir:
Fermat’s last theorem over some small real quadratic fields.
In: Algebra & Number Theory. Vol. 9 (2015) Issue 4 . - pp. 875-895.
ISSN 1937-0652
DOI: https://doi.org/10.2140/ant.2015.9.875

Project information

Project title:
Project's official titleProject's id
Algorithmic and Experimental Methods in Algebra, Geometry and Number TheorySPP 1489

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

Using modularity, level lowering, and explicit computations with Hilbert modular forms, Galois representations, and ray class groups, we show that for 3 ≤ d ≤ 23, where d ≠ 5, 17 and is squarefree, the Fermat equation x^n + y^n = z^n has no nontrivial solutions over the quadratic field ℚ(d) for n ≥ 4. Furthermore, we show that for d = 17, the same holds for prime exponents n ≡ 3,5 (mod 8).

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Fermat; modularity; Galois representation; level lowering
Subject classification: Mathematical Subject Classification 2010: 11D41 (11F80, 11F03)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 12 Apr 2016 07:37
Last Modified: 12 Apr 2016 07:37
URI: https://eref.uni-bayreuth.de/id/eprint/32159