Geodesic
On conditions of expandibility of analytic functions in Dirichlet series
Izvestiya. Mathematics , Tome 6 (1972) no. 6, pp. 1265-1277

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A function $f$, analytic in $\overline D$ or analytic in $D$ and continuous in $\overline D$, where $D$ is an open bounded convex domain, is related to the well-known principle of expansion in Dirichlet series with exponents $\lambda_k$, ($k\geqslant1$) which are the zeros of an entire function of exponential type $L(\lambda)$. Necessary and sufficient conditions on $L(\lambda)$ are given which insure that the series always converges in $D$ to $f(z)$. 
@article{IM2_1972_6_6_a4,
     author = {A. F. Leont'ev},
     title = {On conditions of expandibility of analytic functions in {Dirichlet} series},
     journal = {Izvestiya. Mathematics },
     pages = {1265--1277},
     publisher = {mathdoc},
     volume = {6},
     number = {6},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_6_a4/}
}
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A. F. Leont'ev. On conditions of expandibility of analytic functions in Dirichlet series. Izvestiya. Mathematics , Tome 6 (1972) no. 6, pp. 1265-1277. http://geodesic.mathdoc.fr/item/IM2_1972_6_6_a4/