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.
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
\Bibitem{Bra20}
\by G.~G.~Braichev
\paper On the Lower Indicator of an Entire Function
with Roots of Zero Lower Density Lying on a Ray
\jour Mat. Zametki
\yr 2020
\vol 107
\issue 6
\pages 817--832
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\transl
\jour Math. Notes
\yr 2020
\vol 107
\issue 6
\pages 907--919
\crossref{https://doi.org/10.1134/S0001434620050211}
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Linking options:
https://www.mathnet.ru/eng/mzm12504
https://doi.org/10.4213/mzm12504
https://www.mathnet.ru/eng/mzm/v107/i6/p817
This publication is cited in the following 3 articles:
G. G. Braichev, V. B. Sherstyukov, “On indicator and type of an entire function with roots lying on a ray”, Lobachevskii J Math, 43:3 (2022), 539
K. G. Malyutin, M. V. Kabanko, “On the type of subharmonic functions of finite order”, J Math Sci, 266:6 (2022), 981
G. G. Braichev, V. B. Sherstyukov, “Otsenki indikatorov tseloi funktsii s otritsatelnymi kornyami”, Vladikavk. matem. zhurn., 22:3 (2020), 30–46
Citation in format AMSBIB
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