# Rang de l'image du groupe des unités et polynômes lacunaires

Ranieri, Gabriele. (2007) Rang de l'image du groupe des unités et polynômes lacunaires. Acta arithmetica, Vol. 127. pp. 87-96.

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Official URL: http://edoc.unibas.ch/dok/A5262032

Amorosointroduced a new class of number fields, the so-called class of $PCM$-fields (proche d'un corps $CM$), having interesting arithmetic proprierties. The main result of our work is the proof of the fact that no totally real field is $PCM$. Moreover we show how our proof, in the special case of finite totally real abelian extensions of $mathbb{Q}$, implies a lower bound for the number of non-zero coefficients of polynomials whose certain zeros are roots of $1$.