Geodesic
An estimate for the sum of a Dirichlet series on an arc of bounded slope
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2024), pp. 3-13 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, curve of bounded slope, convergence half-plane.
Mots-clés : maximal term 
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T. I. Belous; A. M. Gaisin; R. A. Gaisin. An estimate for the sum of a Dirichlet series on an arc of bounded slope. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2024), pp. 3-13. http://geodesic.mathdoc.fr/item/IVM_2024_1_a0/

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