This article is cited in 5 papers

An estimate for the Dirichlet series in a half-strip in the case of the irregular distribution of exponents. II

A. M. Gaisin, D. I. Sergeeva

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: 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.

Keywords: order of the Dirichlet series in a half-strip.

UDC: 517.53

Received: 03.05.2005
Revised: 27.04.2007

 English version: Siberian Mathematical Journal, 2008, 49:2, 222–238

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