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This article is cited in 1 scientific paper (total in 1 paper)
An estimate for the sum of a Dirichlet series on an arc of bounded slope
T. I. Belousa, A. M. Gaisinb, R. A. Gaisinb a Ufa University of Science and Technology, 32 Zaky Validy str., Ufa, 450076 Russia
b Institute of Mathematics with Computing Centre – Subdivision of the Ufa Federal Research Centre of Russian Academy of Science, 112 Chernyshevsky str., Ufa, 450008 Russia
Abstract:
The article considers the behavior of the sum of the Dirichlet series $F(s)=\displaystyle \sum\limits_{n} a_ne^{\lambda_ns},$ $0<\lambda_{n}\uparrow\infty, $ which converges absolutely in the left half-plane $\Pi_0$, on a curve arbitrarily approaching the imaginary axis — the boundary of this half-plane. We have obtained a solution to the following problem: Under what additional conditions on $\gamma$ will the strengthened asymptotic relation be valid in the case when the argument $s$ tends to the imaginary axis along $\gamma$ over a sufficiently massive set.
Keywords:
Dirichlet series, lacunary power series, maximal term, curve of bounded slope, convergence half-plane.
Received: 23.12.2022 Revised: 06.02.2023 Accepted: 29.03.2023
Citation:
T. I. Belous, A. M. Gaisin, R. A. Gaisin, “An estimate for the sum of a Dirichlet series on an arc of bounded slope”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 1, 3–13
Linking options:
https://www.mathnet.ru/eng/ivm9946 https://www.mathnet.ru/eng/ivm/y2024/i1/p3
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