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Mat. Sb., 2012, Volume 203, Number 7, Pages 31–56 (Mi msb7879)  

This article is cited in 7 scientific papers (total in 7 papers)

The least type of an entire function of order $\rho\in(0,1)$ having positive zeros with prescribed averaged densities

G. G. Braichev

Moscow State Pedagogical University

Abstract: The problem of the least type of entire functions of order $\rho\in(0,1)$ all of whose zeros lie on the same ray and have the prescribed upper and lower averaged $\rho$-densities is solved. A complete investigation of the value of the extremal type is carried out, including a description of its asymptotic behaviour.
Bibliography: 14 titles.

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

DOI: https://doi.org/10.4213/sm7879

Full text: PDF file (613 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2012, 203:7, 950–975

Bibliographic databases:

UDC: 517.547.2
MSC: 30D15
Received: 21.04.2011 and 05.02.2012

Citation: G. G. Braichev, “The least type of an entire function of order $\rho\in(0,1)$ having positive zeros with prescribed averaged densities”, Mat. Sb., 203:7 (2012), 31–56; Sb. Math., 203:7 (2012), 950–975

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 for the type of an entire function of order less than 1 whose zeros are located on a ray and have given averaged densities Densities”, Dokl. Math., 86:1 (2012), 559–561  crossref  mathscinet  zmath  isi  elib  elib  scopus
    2. G. G. Braichev, “Exact relationships between certain characteristics of growth for complex sequences”, Ufa Math. J., 5:4 (2013), 16–29  mathnet  crossref  elib
    3. O. V. Sherstyukova, “O naimenshem tipe tselykh funktsii poryadka $\rho\in(0,1)$ s nulyami na luche”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 15:4 (2015), 433–441  mathnet  crossref  elib
    4. G. G. Braichev, “The exact bounds of lower type magnitude for entire function of order $\rho\in(0,1)$ with zeros of prescribed average densities”, Ufa Math. J., 7:4 (2015), 32–57  mathnet  crossref  isi  elib
    5. G. G. Braichev, “The least type of an entire function whose zeros have prescribed averaged densities and lie on rays or in a sector”, Sb. Math., 207:2 (2016), 191–225  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. 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
    7. V. B. Sherstyukov, “Asimptoticheskie svoistva tselykh funktsii s zadannym zakonom raspredeleniya kornei”, Kompleksnyi analiz. Tselye funktsii i ikh primeneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 161, VINITI RAN, M., 2019, 104–129  mathnet  mathscinet
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