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Mat. Sb., 2016, Volume 207, Number 2, Pages 45–80 (Mi msb8483)  

This article is cited in 2 scientific papers (total in 2 papers)

The least type of an entire function whose zeros have prescribed averaged densities and lie on rays or in a sector

G. G. Braichev

Moscow State Pedagogical University

Abstract: We consider the problem of the least possible type of entire functions whose zeros have fixed upper and lower averaged densities and lie in a given set. In particular, we solve this problem in several important cases: 1) all zeros lie in a sector, 2) all zeros lie between two straight lines; 3) all zeros lie on rays subdividing the complex plane into equal sectors.
Bibliography: 15 titles.

Keywords: type of an entire function, upper and lower averaged densities of zeros.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00281
The work was supported by the Russian Foundation for Basic Research (grant no. 13-01-00281).


DOI: https://doi.org/10.4213/sm8483

Full text: PDF file (666 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2016, 207:2, 191–225

Bibliographic databases:

UDC: 517.547.22
MSC: Primary 30D15; Secondary 30D10
Received: 01.02.2015 and 07.08.2015

Citation: G. G. Braichev, “The least type of an entire function whose zeros have prescribed averaged densities and lie on rays or in a sector”, Mat. Sb., 207:2 (2016), 45–80; Sb. Math., 207:2 (2016), 191–225

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. Braichev G.G., “Sharp Bounds of Lower Type For Entire Function of Order Rho Is An Element of (0, 1) With Zeroes of Prescribed Average Densities”, Ufa Math. J., 7:4 (2015), 32–57  mathnet  crossref  mathscinet  isi  scopus
    2. G. G. Braichev, V. B. Sherstyukov, “Tochnye otsenki asimptoticheskikh kharakteristik rosta tselykh funktsii s nulyami na zadannykh mnozhestvakh”, Fundament. i prikl. matem., 22:1 (2018), 51–97  mathnet
  • Математический сборник Sbornik: Mathematics (from 1967)
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