Squares in arithmetic progression over number fields

Xavier Xarles

doi:10.1016/j.jnt.2011.07.010

Squares in arithmetic progression over number fields

Xavier Xarles

Departamento de Matemáticas

Producción científica: Contribución a una revista › Artículo › Investigación › revisión exhaustiva

8 Citas (Scopus)

Resumen

We show that there exists an upper bound for the number of squares in arithmetic progression over a number field that depends only on the degree of the field. We show that this bound is 5 for quadratic fields, and also that the result generalizes to k-powers for integers k> 1. © 2011 Elsevier Inc.

Idioma original	Inglés
Páginas (desde-hasta)	379-389
Publicación	Journal of Number Theory
Volumen	132
N.º	3
DOI	https://doi.org/10.1016/j.jnt.2011.07.010
Estado	Publicada - 1 mar 2012

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title = "Squares in arithmetic progression over number fields",

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AB - We show that there exists an upper bound for the number of squares in arithmetic progression over a number field that depends only on the degree of the field. We show that this bound is 5 for quadratic fields, and also that the result generalizes to k-powers for integers k> 1. © 2011 Elsevier Inc.

KW - Arithmetic progression

KW - Gonality

KW - Uniform bounds

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Squares in arithmetic progression over number fields

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