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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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