Geodesic
Growth of entire functions represented by Dirichlet series
Sbornik. Mathematics, Tome 187 (1996) no. 10, pp. 1545-1560 
V. A. Oskolkov; L. I. Kalinichenko. Growth of entire functions represented by Dirichlet series. Sbornik. Mathematics, Tome 187 (1996) no. 10, pp. 1545-1560. http://geodesic.mathdoc.fr/item/SM_1996_187_10_a6/
@article{SM_1996_187_10_a6,
     author = {V. A. Oskolkov and L. I. Kalinichenko},
     title = {Growth of entire functions represented by {Dirichlet} series},
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     year = {1996},
     volume = {187},
     number = {10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_10_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let, $\displaystyle F(z)=\sum _{n=1}^\infty a_ne^{\lambda _nz}$ be an entire function represented in the whole of the plane by an absolutely convergent Dirichlet series such that $$ 0\leqslant \lambda _1<\lambda _2<\dotsb ,\qquad \varlimsup _{n\to \infty }\frac {\ln n}{\lambda _n}=\mu \in [0,+\infty ). $$ The connection between the growth of the quantity $$ M(F;x)=\sup \bigl \{|F(x+iy)|:|y|<+\infty \bigr \},\qquad x\to +\infty. $$ End the behaviour of $|a_n|$ and $\lambda_n$ as $n\to \infty$ is described in general form.

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