Geodesic
An estimate of a~Dirichlet series with real coefficients on~a~ray
Matematičeskie zametki, Tome 60 (1996) no. 6, pp. 810-823.

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Best possible conditions are found under which the logarithm of the absolute value of an entire Dirichlet series with real coefficients rarely changing sign increases on the positive ray in the same way as in the whole plane. This result essentially strengthens a similar result due to Pavlov concerning the growth of Taylor series on the positive ray. 
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A. M. Gaisin. An estimate of a~Dirichlet series with real coefficients on~a~ray. Matematičeskie zametki, Tome 60 (1996) no. 6, pp. 810-823. http://geodesic.mathdoc.fr/item/MZM_1996_60_6_a2/

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