Abstract:
We provide exact two-sided estimates for lower type magnitude of entire functions of order ρ∈(0,1)ρ∈(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.
Citation:
G. G. Braichev, “The exact bounds of lower type magnitude for entire function of order ρ∈(0,1)ρ∈(0,1) with zeros of prescribed average densities”, Ufa Math. J., 7:4 (2015), 32–57
\Bibitem{Bra15}
\by G.~G.~Braichev
\paper The exact bounds of lower type magnitude for entire function of order $\rho\in(0,1)$ with zeros of prescribed average densities
\jour Ufa Math. J.
\yr 2015
\vol 7
\issue 4
\pages 32--57
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\crossref{https://doi.org/10.13108/2015-7-4-32}
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Linking options:
https://www.mathnet.ru/eng/ufa300
https://doi.org/10.13108/2015-7-4-32
https://www.mathnet.ru/eng/ufa/v7/i4/p34
This publication is cited in the following 2 articles:
G. G. Braichev, “On the Connection between the Growth of Zeros and the Decrease of Taylor Coefficients of Entire Functions”, Math. Notes, 113:1 (2023), 27–38
G. G. Braichev, V. B. Sherstyukov, “Sharp bounds for asymptotic characteristics of growth of entire functions with zeros on given sets”, J. Math. Sci., 250:3 (2020), 419–453
Citation in format AMSBIB
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