On three--member power asymptotic of an entire Dirichlet series (in Ukrainian)

Author
L.L.Lugova, M.M.Sheremeta
Ivan Franko National University of Lviv
Abstract
Conditions on the exponents of an entire Dirichlet series $F(z)=\sum_{n=0}^{\infty}a_n e^{(\sigma+it)\lambda_n}$, are found, under which the asymptotic inequalities $ \ln M (\sigma)\le T_1\sigma^{p_1}+T_2\sigma^{p_2}+(\tau+o(1))\sigma^p $ and $ \ln \mu (\sigma)\le T_1\sigma^{p_1}+T_2\sigma^{p_2}+(\tau+o(1))\sigma^p $ as $\sigma \to +\infty $ are equivalent, where $M (\sigma)=\sup\{|F(\sigma +it)|:\,t\in {\Bbb R}\}$, $\mu (\sigma)=\max\{|a_n|\exp(\sigma \lambda_n):n\geq 0\}$ and $p_1>1$, $0 < p < p_2 < p_1$, $T_1>0$, $T_2\in {\Bbb R}\backslash \{0\}$, $\tau \in {\Bbb R}\backslash \{0\}$.
Keywords
three-member power asymptotic, entire Dirichlet series, maximal term, exponent
DOI
doi:10.30970/ms.28.1.37-40
Reference
1. Шеремета М.М., Лугова Л.Л. Тричленна степенева асимптотика логарифма максимального члена цілого ряду Діріхле// Матем.студії. 2006. --Т.25, №2. -- C. 149--168.

2. Sumyk O.M., Sheremeta M.M. On connection between the growth of maximum modulus and maximal term of entire Dirichlet series in term of m-member asymptotics// Matem. studii.\ 2003. -- V. 19, №1. -- P. 83--88.

3. Шеремета М.Н. О поведении максимума модуля целого ряда Дирихле вне исключительного множества// Матем. заметки. -- 1995. -- Т.57, №2. -- C. 283--296.

Pages
37-40
Volume
28
Issue
1
Year
2007
Journal
Matematychni Studii
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