On ternary Diophantine equations of signature (p, p, 2) over number fields
Turkish Journal of Mathematics, cilt.44, sa.4, ss.1197-1211, 2020 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 44 Sayı: 4
- Basım Tarihi: 2020
- Doi Numarası: 10.3906/mat-1911-88
- Dergi Adı: Turkish Journal of Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.1197-1211
- Anahtar Kelimeler: Fermat equation, Generalized fermat equation, Modularity, S-units
- Boğaziçi Üniversitesi Adresli: Evet
Özet
Let K be a totally real number field with narrow class number one and OK be its ring of integers. We prove that there is a constant BK depending only on K such that for any prime exponent p > BK the Fermat type equation xp + yp = z2 with x, y, z ∈ OK does not have certain type of solutions. Our main tools in the proof are modularity, level lowering, and image of inertia comparisons.