On multiplicatively dependent vectors of algebraic numbers
Francesco Pappalardi, Min Sha, Igor E. Shparlinski, Cameron L., Stewart
TL;DR
This paper derives asymptotic formulas for counting multiplicatively dependent vectors of algebraic numbers with fixed degree or within a fixed number field, considering bounded height.
Contribution
It provides new asymptotic formulas for the enumeration of multiplicatively dependent algebraic vectors in specific algebraic settings.
Findings
Derived asymptotic formulas for fixed degree algebraic vectors.
Extended results to vectors within a fixed number field.
Analyzed dependence relations among algebraic numbers.
Abstract
In this paper, we give several asymptotic formulas for the number of multiplicatively dependent vectors of algebraic numbers of fixed degree, or within a fixed number field, and bounded height.
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