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”, Mat. Sb., 2011, Volume 202, Number 12,Pages <nobr>23

This article is cited in 2 papers

An estimate for the sum of a Dirichlet series in terms of the minimum of its modulus on a vertical line segment

A. M. Gaisin^a, Zh. G. Rakhmatullina^b

^a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
^b Bashkir State University

Abstract: 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.

UDC: 517.53+517.537.7

MSC: 30B50, 30D15

Received: 12.04.2010 and 06.09.2011

DOI: 10.4213/sm7725