On logarithm of maximal term of a Dirichlet series converging in a half-plane: three-term power asymptotics |
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| Author |
YuliaStets@mail.ru, m_m_sheremeta@list.ru
Ivan Franko National University of Lviv
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| Abstract |
We have found conditions on
coefficients and
exponents of
Dirichlet series with null abscissa of absolute convergence, under which
the maximal term satisfies the
asymptotic equality $\ln\mu(\sigma,F)$ $=T_{1}|\sigma|^{-\rho_{1}}+T_{2}|\sigma|^{-\rho_{2}}+(\tau+o(1))|\sigma|^{-\rho}
(\sigma\uparrow0)$,
where $T_{1}>0,\ T_{2}\in\mathbb{R}\setminus\{0\},\
\tau\in\mathbb{R}\setminus\{0\},$ $
0<\rho<\rho_{2}<\rho_{1}<+\infty$.
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| Keywords |
Dirichlet series; maximal term; three-term asymptotic
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| Reference |
1. Å. Lindelof, Sur la determination de la croissance des fonctions entieres definies par un development de
Taylor, Bull. Soc. Math., 27 (1903), ¹1, 1–62.
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| Pages |
28-44
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| Volume |
41
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| Issue |
1
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| Year |
2014
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |