The mean values of logarithms of algebraic integers

Dubickas, Artūras

Dubickas, Artūras

Journal de théorie des nombres de Bordeaux, Tome 10 (1998) no. 2, pp. 301-313.

Résumé
Abstract

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

M_{p} (α) = \sqrt[p]{\frac{1}{d} \sum_{i = 1}^{d} | log | α_{i} {| |}^{p}}

où

p > 1

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

M_{p} (α) = \sqrt[p]{\frac{1}{d} \sum_{i = 1}^{d} | log | α_{i} {| |}^{p}}

when

α

is not a root of unity and

p > 1

MR Zbl

@article{JTNB_1998__10_2_301_0,
     author = {Dubickas, Art\={u}ras},
     title = {The mean values of logarithms of algebraic integers},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {301--313},
     publisher = {Universit\'e Bordeaux I},
     volume = {10},
     number = {2},
     year = {1998},
     mrnumber = {1828247},
     zbl = {0923.11145},
     language = {en},
     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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