Artículo
Asymptotic Fermat for signature (4,2,p) over number fields
Fecha de publicación:
09/2023
Editorial:
Academic Press Inc Elsevier Science
Revista:
Journal Of Number Theory
ISSN:
0022-314X
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
Let K be a number field. Using the modular method, we prove asymptotic results on solutions of the Diophantine equation x4−y2=zp over K, assuming some deep but standard conjectures of the Langlands programme when K has at least one complex embedding. On the other hand, we give unconditional results in the case of totally real extensions having odd narrow class number and a unique prime above 2. When modularity of elliptic curves over K is known, for example when K is real quadratic or the r-layer of the cyclotomic Z2-extension of Q, effective asymptotic results hold.
Palabras clave:
FERMAT EQUATIONS
,
MODULAR METHOD
Archivos asociados
Licencia
Identificadores
Colecciones
Articulos(CIEM)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Citación
Villagra Torcomian, Lucas; Asymptotic Fermat for signature (4,2,p) over number fields; Academic Press Inc Elsevier Science; Journal Of Number Theory; 250; 9-2023; 124-138
Compartir
Altmétricas