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

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 $p>1$.

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$.

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author = {Art\={u}ras Dubickas},
title = {The mean values of logarithms of algebraic integers},
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Artūras Dubickas. The mean values of logarithms of algebraic integers. Journal de Théorie des Nombres de Bordeaux, Volume 10 (1998) no. 2, pp. 301-313. doi : 10.5802/jtnb.230. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.230/

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