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Weighted greatest common divisors and weighted heights

Abstract: We introduce the weighted greatest common divisor of a tuple of integers and explore some of its basic properties. Furthermore, for a set of weights w=(q0,...,qn), we use the concept of the weighted greatest common divisor to define a height h(p) on weighted projective spaces WPwn(k). We prove some of the basic properties of this weighted height, including an analogue of the Northcott's theorem for heights on projective spaces.

 Autoría: Beshaj L., Gutierrez J., Shaska T.,

 Fuente: Journal of Number Theory, 2020, 213, 319-346

 Editorial: Elsevier

 Fecha de publicación: 01/08/2020

 Nº de páginas: 28

 Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.jnt.2019.12.012

 ISSN: 0022-314X,1096-1658

 Url de la publicación: https://doi.org/10.1016/j.jnt.2019.12.012