有界斜率弧上狄利克特数列之和的估计值

T. Belous, A. M. Gaisin, R. A. Gaisin
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引用次数: 0

摘要

文章考虑了迪里希勒数列 F(s) = \sum nane\lambda ns, 0 < \lambda n \uparrow \infty 的和的行为,它在左半平面 \Pi 0 中绝对收敛于任意接近虚轴--这个半平面的边界--的曲线上。我们得到了下面问题的一个解:当参数 s 在一个足够大的集合上沿着 \gamma 趋向于虚轴时,在 \gamma 的哪些附加条件下,加强的渐近关系将有效。
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An estimate for the sum of a Dirichlet series on an arc of bounded slope
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.
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