Estimates of the maximal term of entire Dirichlet series in terms of two-member asymptotics |
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| Author |
Faculty of Mechanics and Mathematics, Lviv National University
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| Abstract |
Conditions on coefficients and exponents of an entire Dirichlet series
are found in order that the logarithm of the maximal term $\mu(\sigma,F)$ admits
an upper estimate of the form
$\ln\,\mu(\sigma,F)\le\Phi_1(\sigma)+(1+o(1))\tau\Phi_2(\sigma)$ as $\sigma\to +\|$,
and the same lower estimate, where $\tau$ is a real number,
$\Phi_1$, $\Phi_2$ are positive functions satisfying some condtions.
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| Keywords |
entire Dirichlet series, coefficients and exponents conditions, upper and lower estimates, logarithm of maximal term, growth of entire functions, asymptotic inequalities, complex analysis
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| DOI |
doi:10.30970/ms.14.2.159-164
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Reference |
1. Sheremeta M. M., Sumyk O. M. A connection between the growth of Young conjugated functions, Matematychni studii 11 (1999), no.1, 41–47 (in Ukrainian).
2. Zabolotskyi M. V., Sheremeta M. M. A generalization of Lindelöf theorem, Ukr. matem. journ. 50 (1998), no.9, 1177–1192 (in Ukrainian). |
| Pages |
159-164
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| Volume |
14
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| Issue |
2
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| Year |
2000
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| Journal |
Matematychni Studii
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| Full text of paper | |
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