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Ufimsk. Mat. Zh., 2015, Volume 7, Issue 4, Pages 34–60 (Mi ufa300)  

This article is cited in 1 scientific paper (total in 1 paper)

The exact bounds of lower type magnitude for entire function of order $\rho\in(0,1)$ with zeros of prescribed average densities

G. G. Braichev

Moscow State Pedagogical University, Moscow, Russia

Abstract: We provide exact two-sided estimates for lower type magnitude of entire functions of order $\rho\in(0,1)$. The zeroes of these functions have prescribed upper and lower average densities and are arbitrarily distributed in the complex plane or on a ray. We analyze the obtained results and compare them them with known facts for entire functions of usual type.

Keywords: type and lower type of an entire function, the upper and lower average densities of the sequence of zeroes.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00281


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English version:
Ufa Mathematical Journal, 2015, 7:4, 32–57 (PDF, 469 kB); https://doi.org/10.13108/2015-7-4-32

Bibliographic databases:

UDC: 517.521+517.547.22
MSC: 30D15
Received: 22.10.2015

Citation: 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”, Ufimsk. Mat. Zh., 7:4 (2015), 34–60; Ufa Math. J., 7:4 (2015), 32–57

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
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