I‑AIMS Institute for Artificial Intelligence
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Weighted greatest common divisors and weighted heights

Lubjana Beshaj, Jaime Gutierrez, Tanush Shaska

I-AIMS paper 2019-1 Β· Published in J. Number Theory 213 (2020), 319–346 Β· 2020

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 = (qβ‚€, …, qβ‚™), we use the concept of the weighted greatest common divisor to define a height π”₯(𝔭) on weighted projective spaces π•Žβ„™βΏ_𝔴(k), over a field k. We prove some of the basic properties of this weighted height, including an analogue of Northcott’s theorem for heights on projective spaces.

MSC classes: Primary 11G50; Secondary 14H10, 14H45, 14G40

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