C Stewart
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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
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https://doi.org/10.46298/hrj.2020.6603
Multiplicatively dependent vectors with coordinates algebraic numbersArticle
Authors: C Stewart 1
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C Stewart
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).