Geodesic
An estimate for a~Dirichlet series whose exponents are zeros of an~entire function with irregular behavior
Sbornik. Mathematics, Tome 81 (1995) no. 1, pp. 163-183

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Under sufficiently general assumptions an estimate is obtained of the sum of an entire Dirichlet series in terms of the maximum of its modulus on a vertical segment. An analogous estimate is obtained for the Dirichlet series converging only in a half-plane. 
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A. M. Gaisin. An estimate for a~Dirichlet series whose exponents are zeros of an~entire function with irregular behavior. Sbornik. Mathematics, Tome 81 (1995) no. 1, pp. 163-183. http://geodesic.mathdoc.fr/item/SM_1995_81_1_a8/