On convergence and growth of multiple Dirichlet series (Q650340)
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scientific article; zbMATH DE number 5980716
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On convergence and growth of multiple Dirichlet series |
scientific article; zbMATH DE number 5980716 |
Statements
On convergence and growth of multiple Dirichlet series (English)
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25 November 2011
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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)].
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\(n\)-tuple Dirichlet series
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convergent abscissa
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maximal module
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maximal term
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order
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