On abelian multiplicatively dependent points on a curve in a torus

Alina Ostafe, Min Sha*, Igor E. Shparlinski, Umberto Zannier

*Corresponding author for this work

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We show, under some natural conditions, that the set of abelian (and thus also cyclotomic) multiplicatively dependent points on an irreducible curve over a number field is a finite union of preimages of roots of unity by a certain finite set of primitive characters from Gmn to Gm restricted to the curve, and a finite set. We also introduce the notion of primitive multiplicative dependence and obtain a finiteness result for primitively multiplicatively dependent points defined over a so-called Bogomolov extension of a number field.

Original languageEnglish
Pages (from-to)391-401
Number of pages11
JournalQuarterly Journal of Mathematics
Volume69
Issue number2
DOIs
Publication statusPublished - 1 Jun 2018

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