Geodesic
On the Growth of Entire Functions of Exponential Type near a Straight Line
Matematičeskie zametki, Tome 70 (2001) no. 4, pp. 621-635

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Let $\Lambda =\{\lambda _n\}$ be a sequence of complex numbers such that $\lambda _n\to\infty$, as $n\to+\infty$. For $\Lambda$ close to the imaginary axis, upper bounds of the indicator of a nonzero entire function of exponential type with minimal growth vanishing on $\Lambda$ is obtained. These bounds give sufficient conditions for the system of exponents to be incomplete in an unbounded domain in $\{\exp(\lambda _nz)\}$. 
@article{MZM_2001_70_4_a13,
     author = {B. N. Khabibullin},
     title = {On the {Growth} of {Entire} {Functions} of {Exponential} {Type} near a {Straight} {Line}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {621--635},
     publisher = {mathdoc},
     volume = {70},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a13/}
}
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B. N. Khabibullin. On the Growth of Entire Functions of Exponential Type near a Straight Line. Matematičeskie zametki, Tome 70 (2001) no. 4, pp. 621-635. http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a13/