Estimates of the maximal term of entire Dirichlet series in terms of two-member asymptotics

Author
M. M. Sheremeta
Faculty of Mechanics and Mathematics, Lviv National University
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.
Keywords
entire Dirichlet series, coefficients and exponents conditions, upper and lower estimates, logarithm of maximal term, growth of entire functions, asymptotic inequalities, complex analysis
DOI
doi:10.30970/ms.14.2.159-164
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
Volume
14
Issue
2
Year
2000
Journal
Matematychni Studii
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