The mean values of logarithms of algebraic integers
Journal de Théorie des Nombres de Bordeaux, Tome 10 (1998) no. 2, pp. 301-313.

Soit ${\alpha }_{1}=\alpha ,{\alpha }_{2},\cdots ,{\alpha }_{d}$ l’ensemble des conjugués d’un entier algébrique $\alpha$ de degré $d$, n’étant pas une racine de l’unité. Dans cet article on propose de minorer

 ${M}_{p}\left(\alpha \right)=\sqrt[p]{\frac{1}{d}{\sum }_{i=1}^{d}|log|{\alpha }_{i}{||}^{p}}$
$p>1$.

Let $\alpha$ be an algebraic integer of degree $d$ with conjugates ${\alpha }_{1}=\alpha ,{\alpha }_{2},\cdots ,{\alpha }_{d}$. In the paper we give a lower bound for the mean value

 ${M}_{p}\left(\alpha \right)=\sqrt[p]{\frac{1}{d}{\sum }_{i=1}^{d}|log|{\alpha }_{i}{||}^{p}}$
when $\alpha$ is not a root of unity and $p>1$.

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title = {The mean values of logarithms of algebraic integers},
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year = {1998},
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url = {http://www.numdam.org/item/JTNB_1998__10_2_301_0/}
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Dubickas, Artūras. The mean values of logarithms of algebraic integers. Journal de Théorie des Nombres de Bordeaux, Tome 10 (1998) no. 2, pp. 301-313. http://www.numdam.org/item/JTNB_1998__10_2_301_0/

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