# ANNALES DE L'INSTITUT FOURIER

The deficiency of entire functions with Fejér gaps
Annales de l'Institut Fourier, Volume 33 (1983) no. 3, pp. 39-58.

We say that an entire function $f\left(z\right)={\sum }_{k=0}{a}_{k}{z}^{{n}_{k}}\phantom{\rule{3.33333pt}{0ex}}\left(0={n}_{0}<{n}_{1}<{n}_{2}<...\right)$ has Fejér gaps if ${\sum }_{k=1}^{\infty }1/{n}_{k}<\infty .$ The main result of this paper is as follows: An entire function with Fejér gaps has no finite deficient value.

On dit qu’une fonction entière $f\left(z\right)={\sum }_{k=0}{a}_{k}{z}^{{n}_{k}}\phantom{\rule{3.33333pt}{0ex}}\left(0={n}_{0}<{n}_{1}<{n}_{2}<...\right)$ a des lacunes de Fejér si ${\sum }_{k=1}^{\infty }1/{n}_{k}<\infty .$ Le résultat principal de cet article est le suivant : Une fonction entière avec des lacunes de Fejér n’a pas de valeur déficiente finie.

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Murai, Takafumi. The deficiency of entire functions with Fejér gaps. Annales de l'Institut Fourier, Volume 33 (1983) no. 3, pp. 39-58. doi : 10.5802/aif.930. https://aif.centre-mersenne.org/articles/10.5802/aif.930/

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