The deficiency of entire functions with Fejér gaps
Murai, Takafumi
Annales de l'Institut Fourier, Tome 33 (1983), p. 39-58 / Harvested from Numdam
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On dit qu’une fonction entière f(z)=∑ k=0 a k z n k (0=n 0 <n 1 <n 2 <...) a des lacunes de Fejér si ∑ k=1 ∞ 1/n k <∞. Le résultat principal de cet article est le suivant : Une fonction entière avec des lacunes de Fejér n’a pas de valeur déficiente finie.

We say that an entire function f(z)=∑ k=0 a k z n k (0=n 0 <n 1 <n 2 <...) has Fejér gaps if ∑ k=1 ∞ 1/n k <∞. The main result of this paper is as follows: An entire function with Fejér gaps has no finite deficient value.

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     author = {Murai, Takafumi},
     title = {The deficiency of entire functions with Fej\'er gaps},
     journal = {Annales de l'Institut Fourier},
     volume = {33},
     year = {1983},
     pages = {39-58},
     doi = {10.5802/aif.930},
     mrnumber = {84m:30046},
     zbl = {0489.30028},
     mrnumber = {723947},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1983__33_3_39_0}
}

Murai, Takafumi. The deficiency of entire functions with Fejér gaps. Annales de l'Institut Fourier, Tome 33 (1983) pp. 39-58. doi : 10.5802/aif.930. http://gdmltest.u-ga.fr/item/AIF_1983__33_3_39_0/

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