C Stewart - Multiplicatively dependent vectors with coordinates algebraic numbers

hrj:6603 - Hardy-Ramanujan Journal, June 29, 2020, Volume 42 - Special Commemorative volume in honour of Alan Baker - 2019 - https://doi.org/10.46298/hrj.2020.6603
Multiplicatively dependent vectors with coordinates algebraic numbersArticle

Authors: C Stewart 1

  • 1 University of Waterloo [Waterloo]

We shall prove that close to each point in \mathbb{C}^n with coordinates of comparable size there is a point (t_1 , ... , t_n) with the property that no multiplicatively dependent vector (u_1 , ... , u_n) with coordinates which are algebraic numbers of height at most H and degree at most d is very close to (t_1 , ... , t_n).


Volume: Volume 42 - Special Commemorative volume in honour of Alan Baker - 2019
Published on: June 29, 2020
Accepted on: June 29, 2020
Submitted on: June 29, 2020
Keywords: Multiplicatively dependent vectors,heights,2010 MSC: 11N25, 11R04,[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
Funding:
    Source : OpenAIRE Graph
  • Funder: Natural Sciences and Engineering Research Council of Canada

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