Work

An estimate for the sum of a Dirichlet series on an arc of bounded slope

Year: 2024

Type: article

Abstract: The article considers the behavior of the sum of the Dirichlet series F(s) = \sum nane\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.

Source: Russian Mathematics

DOI: 10.26907/0021-3446-2024-1-3-13

Authors: T. I. Belous, A. M. Gaisin, R. A. Gaisin

Institutions: Ufa University of Science and Technology, Russian Academy of Sciences, Institute of Mathematics with Computer Center

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W4391786239

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Cites: 3

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Related to: 10