Polynomial relations amongst algebraic units of low measure
Volume 164 / 2014
Acta Arithmetica 164 (2014), 25-30
MSC: Primary 11R09; Secondary 11G50.
DOI: 10.4064/aa164-1-2
Abstract
For an algebraic number field $\mathbb K$ and a subset $\{\alpha _1, \ldots , \alpha _r \} \subseteq \mathcal {O}_{\mathbb K}$, we establish a lower bound for the average of the logarithmic heights that depends on the ideal of polynomials in $\mathbb Q[x_1, \ldots , x_r]$ vanishing at the point $(\alpha _1, \ldots , \alpha _r )$.
