Year: 2015
Type: article
Abstract: Using modularity, level lowering, and explicit computations with Hilbert modular forms, Galois representations, and ray class groups, we show that for 3 Ä d Ä 23, where d ¤ 5; 17 and is squarefree, the Fermat equation x n C y n D z n has no nontrivial solutions over the quadratic field .ޑ p d/ for n 4. Furthermore, we show that for d D 17, the same holds for prime exponents n Á 3; 5 .mod8/.
Source: Algebra & Number Theory
Authors: Nuno Freitas, Samir Siksek
Institutions: University of Bayreuth, University of Warwick
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1607574071