Regularity of the Growth of Dirichlet Series with respect to a Strongly Incomplete Exponential System

The article deals with the behavior of the sum of the Dirichlet series , with , converging absolutely in the left half-plane along a curve arbitrarily approaching the imaginary axis, the boundary of this half-plane. We assume that the maximal term of the series satisfies some lower estimate on some...

Full description

Saved in:
Bibliographic Details
Published in:Siberian mathematical journal 2023-07, Vol.64 (4), p.854-863
Main Authors: Gaisin, A. M., Gaisin, R. A., Belous, T. I.
Format: Article
Language:English
Subjects:
Asymptotic properties
Dirichlet problem
Half planes
Mathematics
Mathematics and Statistics
Questions
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The article deals with the behavior of the sum of the Dirichlet series , with , converging absolutely in the left half-plane along a curve arbitrarily approaching the imaginary axis, the boundary of this half-plane. We assume that the maximal term of the series satisfies some lower estimate on some sequence of points . The essence of the questions we consider is as follows: Given a curve  starting from the half-plane  and ending asymptotically approaching on the boundary of  , what are the conditions for the existence of a sequence , with , such that , where ? A.M. Gaisin obtained the answer to this question in 2003. In the present article, we solve the following problem: Under what additional conditions on is the finer asymptotic relation valid in the case that the argument  tends to the imaginary axis along over a sufficiently massive set?
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446623040079