# The mean values of logarithms of algebraic integers

• Volume: 10, Issue: 2, page 301-313
• ISSN: 1246-7405

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## Abstract

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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 $p>1$.

## How to cite

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Dubickas, Artūras. "The mean values of logarithms of algebraic integers." Journal de théorie des nombres de Bordeaux 10.2 (1998): 301-313. <http://eudml.org/doc/248169>.

@article{Dubickas1998,
abstract = {Let $\alpha$ be an algebraic integer of degree $d$ with conjugates $\alpha _1 = \alpha , \alpha _2, \dots , \alpha _d$. In the paper we give a lower bound for the mean value\begin\{equation*\} M\_p(\alpha )=\@root p \of \{\frac\{1\}\{d\} \sum ^\{d\}\_\{i=1\}|\log |\alpha \_i||^p\}\end\{equation*\}when $\alpha$ is not a root of unity and $p &gt; 1$.},
author = {Dubickas, Artūras},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {Mahler's measure; logarithms of algebraic integers; mean values of logarithms},
language = {eng},
number = {2},
pages = {301-313},
publisher = {Université Bordeaux I},
title = {The mean values of logarithms of algebraic integers},
url = {http://eudml.org/doc/248169},
volume = {10},
year = {1998},
}

TY - JOUR
AU - Dubickas, Artūras
TI - The mean values of logarithms of algebraic integers
JO - Journal de théorie des nombres de Bordeaux
PY - 1998
PB - Université Bordeaux I
VL - 10
IS - 2
SP - 301
EP - 313
AB - Let $\alpha$ be an algebraic integer of degree $d$ with conjugates $\alpha _1 = \alpha , \alpha _2, \dots , \alpha _d$. In the paper we give a lower bound for the mean value\begin{equation*} M_p(\alpha )=\@root p \of {\frac{1}{d} \sum ^{d}_{i=1}|\log |\alpha _i||^p}\end{equation*}when $\alpha$ is not a root of unity and $p &gt; 1$.
LA - eng
KW - Mahler's measure; logarithms of algebraic integers; mean values of logarithms
UR - http://eudml.org/doc/248169
ER -

## References

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