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Polynomial relations amongst algebraic units of low measure

Volume 164 / 2014

John Garza Acta Arithmetica 164 (2014), 25-30 MSC: Primary 11R09; Secondary 11G50. DOI: 10.4064/aa164-1-2


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 $(\alpha _1, \ldots , \alpha _r )$.


  • John GarzaDrake University
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    Des Moines, IA 50311, U.S.A.

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