On convergence and growth of multiple Dirichlet series
type: Item
instance of: scholarly article
title: On convergence and growth of multiple Dirichlet series
zbMATH Open document ID: 1244.30004
DOI: 10.1134/S000143461011012X
author: Meili Liang
author: Zongsheng Gao
published in: Mathematical Notes
publication date: 2011-11-25T00:00:00Z
review text: In [``On the convergence of double Dirichlet series and double Laplace transform'' (Chinese), J. Wuhan Univ., Nat. Sci. Ed. 1, No. 1, 1--16 (1962)], \textit{J. Yu} extended Valiron's formula to double Dirichlet series. In the present paper, the authors extend Valiron's formula to \(n\)-tuple Dirichlet series and establish a relation between the order of any \(n\)-tuple Dirichlet series and its coefficients, extending some results concerning the convergence of multiple Taylor series in [\textit{J. Yu}, Acta Math. Sci., Ser. B, Engl. Ed. 26, No. 3, 568--576 (2006; Zbl 1101.32001)].
Mathematics Subject Classification ID: 30B50
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 5980716
zbMATH Keywords: \(n\)-tuple Dirichlet series
zbMATH Keywords: convergent abscissa
zbMATH Keywords: maximal module
zbMATH Keywords: maximal term
zbMATH Keywords: order
reviewed by: Yinying Kong
MaRDI profile type: Publication
cites work: Q3834794
cites work: Q3312454
cites work: Julia lines of random Dirichlet series
cites work: Q3312453
cites work: Some properties of multiple Taylor series and random Taylor series
description: scientific article; zbMATH DE number 5980716