Sbornik. Mathematics, Tome 45 (1983) no. 3, pp. 411-422
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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/
@article{SM_1983_45_3_a5,
author = {A. M. Gaisin},
title = {A bound for the growth in a half-strip of a~function represented by {a~Dirichlet} series},
journal = {Sbornik. Mathematics},
pages = {411--422},
year = {1983},
volume = {45},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1983_45_3_a5/}
}
TY - JOUR
AU - A. M. Gaisin
TI - A bound for the growth in a half-strip of a function represented by a Dirichlet series
JO - Sbornik. Mathematics
PY - 1983
SP - 411
EP - 422
VL - 45
IS - 3
UR - http://geodesic.mathdoc.fr/item/SM_1983_45_3_a5/
LA - en
ID - SM_1983_45_3_a5
ER -
%0 Journal Article
%A A. M. Gaisin
%T A bound for the growth in a half-strip of a function represented by a Dirichlet series
%J Sbornik. Mathematics
%D 1983
%P 411-422
%V 45
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1983_45_3_a5/
%G en
%F SM_1983_45_3_a5
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.
