Mathematical Research Letters

Volume 30 (2023)

Number 2

On the distribution of multiplicatively dependent vectors

Pages: 509 – 540

DOI: https://dx.doi.org/10.4310/MRL.2023.v30.n2.a7

Authors

Sergei V. Konyagin (Steklov Mathematical Institute, Moscow, Russia)

Min Sha (School of Mathematical Sciences, South China Normal University, Guangzhou, China)

Igor E. Shparlinski (Department of Pure Mathematics, University of New South Wales, Sydney, NSW, Australia)

Cameron L. Stewart (Department of Pure Mathematics, University of Waterloo, Ontario, Canada)

Abstract

In this paper, we study the distribution of multiplicatively dependent vectors. For example, although they have zero Lebesgue measure, they are everywhere dense both in $\mathbb{R}^n$ and $\mathbb{C}^n$. We also study this property in a more detailed manner by considering the covering radius of such vectors.

Received 23 March 2019

Received revised 21 November 2022

Accepted 24 January 2023

Published 13 September 2023