Geodesic
A bound for the growth in a half-strip of a~function represented by a~Dirichlet series
Sbornik. Mathematics, Tome 45 (1983) no. 3, pp. 411-422

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For a function defined by a Dirichlet series that converges in a right half-plane, we introduce the $R$-order $\rho$ in the half-plane and the $R$-order $\rho_s$ in a half-strip $S=\{s=\sigma+it:\sigma>0,\ |t|$. Under certain restrictions on the width of the half-strip, we obtain the inequalities $\rho_s\leqslant\rho\leqslant\rho_s+q$, where $q$ is defined by a sequence of powers. The two extreme inequalities are sharp. Bibliography: 3 titles. 
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     author = {A. M. Gaisin},
     title = {A bound for the growth in a half-strip of a~function represented by {a~Dirichlet} series},
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A. M. Gaisin. A bound for the growth in a half-strip of a~function represented by a~Dirichlet series. Sbornik. Mathematics, Tome 45 (1983) no. 3, pp. 411-422. http://geodesic.mathdoc.fr/item/SM_1983_45_3_a5/