On the number of integer polynomials with multiplicatively dependent roots

2017/07/17 by Artūras Dubickas, Min Sha, Dubickas, Arturas +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1707.04965

openalex publication_date 2017/07/17 · openalex created_date 2017/07/31 · openalex updated_date 2026/07/28

Abstract

In this paper, we give some counting results on integer polynomials of fixed degree and bounded height whose distinct non-zero roots are multiplicatively dependent. These include sharp lower bounds, upper bounds and asymptotic formulas for various cases, although in general there is a logarithmic gap between lower and upper bounds.

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