Geodesic
A necessary condition for all the~zeros of an~entire function of exponential type to lie in a~curvilinear half-plane
Sbornik. Mathematics, Tome 186 (1995) no. 9, pp. 1353-1362

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Under the assumption that the integral $$ \int_{\mathbb R}\frac{\log|F(x)|}{1+x^2}\,dx $$ exists, a condition necessary for all the zeros of the entire function $F(z)$ of exponential type to lie in the curvilinear half-plane $\operatorname{Im}z\leqslant\ (\geqslant)\ h(|\operatorname{Re}z|)$ (where $h(t)$ is a regularly varying function) is obtained. 
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     author = {A. M. Sedletskii},
     title = {A necessary condition for all the~zeros of an~entire function of exponential type to lie in a~curvilinear half-plane},
     journal = {Sbornik. Mathematics},
     pages = {1353--1362},
     publisher = {mathdoc},
     volume = {186},
     number = {9},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_9_a7/}
}
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A. M. Sedletskii. A necessary condition for all the~zeros of an~entire function of exponential type to lie in a~curvilinear half-plane. Sbornik. Mathematics, Tome 186 (1995) no. 9, pp. 1353-1362. http://geodesic.mathdoc.fr/item/SM_1995_186_9_a7/