An estimate for the sum of a~Dirichlet series in terms of the minimum of its modulus on a~vertical line segment
Sbornik. Mathematics, Tome 202 (2011) no. 12, pp. 1741-1773
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The behaviour of the sum of an entire Dirichlet series is analyzed in terms of the minimum of its modulus on a system of vertical line segments. Also a more general problem, connected with the Pólya conjecture is posed and solved. It concerns the minimum modulus of an entire function with Fabri gaps and its growth along curves going to infinity.
Bibliography: 33 titles.
Keywords:
Dirichlet series, minimum modulus, Fejér gaps.
@article{SM_2011_202_12_a1,
author = {A. M. Gaisin and Zh. G. Rakhmatullina},
title = {An estimate for the sum of {a~Dirichlet} series in terms of the minimum of its modulus on a~vertical line segment},
journal = {Sbornik. Mathematics},
pages = {1741--1773},
publisher = {mathdoc},
volume = {202},
number = {12},
year = {2011},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2011_202_12_a1/}
}
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%0 Journal Article %A A. M. Gaisin %A Zh. G. Rakhmatullina %T An estimate for the sum of a~Dirichlet series in terms of the minimum of its modulus on a~vertical line segment %J Sbornik. Mathematics %D 2011 %P 1741-1773 %V 202 %N 12 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_2011_202_12_a1/ %G en %F SM_2011_202_12_a1
A. M. Gaisin; Zh. G. Rakhmatullina. An estimate for the sum of a~Dirichlet series in terms of the minimum of its modulus on a~vertical line segment. Sbornik. Mathematics, Tome 202 (2011) no. 12, pp. 1741-1773. http://geodesic.mathdoc.fr/item/SM_2011_202_12_a1/