Northcott numbers for the weighted Weil heights
Masao Okazaki, Kaoru Sano
TL;DR
This paper investigates the distribution of Northcott numbers for weighted Weil heights, extending previous work on absolute and relative Weil heights and refining existing results in the field.
Contribution
It provides a comprehensive analysis of Northcott numbers for weighted Weil heights, generalizing prior concepts and refining earlier findings.
Findings
Distribution of Northcott numbers for weighted Weil heights characterized.
Results unify and extend previous understanding of Weil height distributions.
Refinement of earlier results by Pazuki, Technau, and Widmer.
Abstract
We answer the question of Vidaux and Videla about the distribution of the Northcott numbers for the Weil height. We solve the same problem for the weighted Weil heights. These heights generalize both the absolute and relative Weil height. Our results also refine those of Pazuki, Technau, and Widmer.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Analytic Number Theory Research