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arXiv · 1902.06563

Weighted greatest common divisors and weighted heights

Lubjana Beshaj·Jaime Gutierrez·Tony Shaska
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Abstract

We introduce the weighted greatest common divisor of a tuple of integers and explore some of it basic properties. Furthermore, for a set of heights $\mathfrak w=(q_0, \ldots , q_n)$, we use the concept of the weighted greatest common divisor to define a height $\mathfrak{h} (\mathfrak p)$ on weighted projective spaces $\mathbb{WP}_{\mathfrak w}^n (k)$. We prove some of the basic properties of this weighted height, including an analogue of the Northcott's theorem for heights on projective spaces.

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Lubjana Beshaj, Jaime Gutierrez, Tony Shaska. 2019-02-18. Weighted greatest common divisors and weighted heights. https://arxiv.org/abs/1902.06563

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