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Matematicheskie Zametki, 2020, Volume 107, Issue 6, Pages 817–832
DOI: https://doi.org/10.4213/mzm12504 (Mi mzm12504) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On the Lower Indicator of an Entire Function with Roots of Zero Lower Density Lying on a Ray

G. G. Braichev

Moscow State Pedagogical University
Full-text PDF (525 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm12504
Abstract: The paper deals with an entire function of noninteger order with a sequence of negative roots having (for this order) zero lower and finite upper densities. Sharp estimates for the lower indicator of such a function are obtained. It is proved that, in some angles, this characteristic is identically zero, and its form in the other angles is obtained provided that the sequence of roots of the entire function sufficiently rapidly tends to infinity.
Keywords: entire function, type and lower type of a function, indicator and lower indicator, upper and lower densities of a set of roots, completely regular growth.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00236
This work was supported by the Russian Foundation for Basic Research under grant 18-01-00236.
Received: 03.07.2019
Revised: 16.01.2020
English version:
Mathematical Notes, 2020, Volume 107, Issue 6, Pages 907–919
DOI: https://doi.org/10.1134/S0001434620050211
Bibliographic databases:
Document Type: Article
UDC: 517.547.22
Language: Russian
Citation: G. G. Braichev, “On the Lower Indicator of an Entire Function with Roots of Zero Lower Density Lying on a Ray”, Mat. Zametki, 107:6 (2020), 817–832; Math. Notes, 107:6 (2020), 907–919
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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