Northcott numbers for generalized weighted Weil heights
Masao Okazaki, Kaoru Sano
TL;DR
This paper introduces a generalized form of weighted Weil heights, extending existing heights, and studies their Northcott numbers, with applications to spectral heights on matrices, advancing understanding in height theory.
Contribution
The paper generalizes weighted Weil heights and analyzes their Northcott numbers, extending previous work and applying results to spectral heights on matrices.
Findings
Generalized weighted Weil heights encompass Weil's and Dobrowolski's heights.
Established bounds and properties of Northcott numbers for these heights.
Applied results to evaluate Northcott numbers for Talamanca's spectral height.
Abstract
We give a generalization of weighted Weil heights. These heights generalize both Weil's heights and Dobrowolski's height. We study Northcott numbers for our heights. Our results generalize the authors' former work on Vidaux and Videla's question about the Northcott number. As an application, we evaluate Northcott numbers for Talamanca's spectral height on matrices.
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Taxonomy
TopicsAdvanced Topics in Algebra · Graph theory and applications · Advanced Algebra and Geometry