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An estimate for the Dirichlet series in a half-strip in the case of the irregular distribution of exponents. II. (Russian, English) Zbl 1164.30307

Sib. Mat. Zh. 49, No. 2, 280-298 (2008); translation in Sib. Math. J. 49, No. 2, 222-238 (2008).
Summary: We study the Dirichlet series that are convergent only in a half-plane and whose sequence of exponents extends to a ‘regular’ sequence. We establish some unimprovable estimates for the order of the sum of the Dirichlet series in a half-strip whose width depends on the special distribution density of the exponents.

MSC:

30B50 Dirichlet series, exponential series and other series in one complex variable
30D15 Special classes of entire functions of one complex variable and growth estimates
30E10 Approximation in the complex plane
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