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Mat. Sb., 2011, Volume 202, Number 12, Pages 23–56 (Mi msb7725)  
This article is cited in 2 scientific papers (total 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. Gaisina, Zh. G. Rakhmatullinab†

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.
† Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm7725

Full text: PDF file (760 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2011, 202:12, 1741–1773

Bibliographic databases:

UDC: 517.53+517.537.7
MSC: 30B50, 30D15
Received: 12.04.2010 and 06.09.2011

Citation: 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., 202:12 (2011), 23–56; Sb. Math., 202:12 (2011), 1741–1773

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. M. Gaisin, “Minimum of modulus of the sum of Dirichlet series converging in a half-plane”, Ufa Math. J., 5:4 (2013), 49–57  mathnet  crossref  elib
    2. A. M. Gaisin, G. A. Gaisina, “Estimate for growth and decay of functions in Macintyre–Evgrafov kind theorems”, Ufa Math. J., 9:3 (2017), 26–36  mathnet  crossref  isi  elib
    		• Математический сборник Sbornik: Mathematics (from 1967)
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