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Discrete Limit Theorems for General Dirichlet Series. II
Lithuanian Mathematical Journal, 2004A Dirichlet series \(f(s)=\sum_{m=1}^\infty a_m e^{-\lambda_m s}\) is considered with real \(\lambda_m>c(\log m)^\delta\), \(f(\sigma+it)=O(| t| ^\alpha)\), \(\alpha>0\) as \(| t| \to\infty\), \(\int_{-T}^T| f(\sigma+it)| ^2\,dt=O(T) \to\infty\). Denote \[ \mu(A)={1\over N+1}\text{card}\{f(\sigma+imh)\in A;\;m=0,1,\dots, N\}. \] It is shown that if \(\{
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Absolute convergence of general multiple dirichlet series
Research in Number Theory, 2023In this paper, the author studies the absolute convergence of general multiple Dirichlet series defined by \[ \Phi_r((s_j); (a_j))= \sum_{m_1=1}^\infty\sum_{m_2=1}^\infty\cdots\sum_{m_r=1}^\infty\frac{a_1(m_1)a_2(m_2)\cdots a_r(m_r)}{m_1^{s_1}(m_1+m_2)^{s_2}\cdots (m_1+m_2+\cdots+m_r)^{s_r}}, \] where \(a_i\) are arithmetic functions.
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General Properties of Dirichlet Series
2013For a real number θ, we denote by ℂ θ the following vertical half-plane: $${\mathbb{C}_\theta } = \left\{ {s \in \mathbb{C};\Re es > \theta } \right\}$$ .
Hervé Queffélec, Martine Queffélec
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Joint universality of general Dirichlet series
Izvestiya: Mathematics, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The universality of general Dirichlet series
Analysis, 2003The series \(f(s)=\sum_{m=1}^\infty a_m{e}^{-\lambda_ms}\), where \(a_m\in \mathbb C\) and \(\lambda_m\in\mathbb R: \lim_{m\to\infty}=+\infty\), is called a general Dirichlet series with coefficients \(a_m\) and exponents \(\lambda_m\). The authors continue the investigations of \textit{S.~M.~Gonek} [Analytic properties of zeta and L-functions. Ph.
Laurinčikas, Antanas +2 more
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REPRESENTATION OF FUNCTIONS BY GENERALIZED DIRICHLET SERIES
Russian Mathematical Surveys, 1969This article is concerned with the representation of functions in domains of the complex plain by series in the systems , , .In § 1 we construct systems biorthogonal to the systems , , and find the asymptotic behaviour of functions of these systems.In § 2 we determine in a natural way the coefficients of the series in the systems in question by means ...
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The generalized lower order of Dirichlet series
Acta Mathematica Scientia, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Qingyuan, Huo, Yingying
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Dirichlet Series and Generating Functions
1986A series of the form $$ \sum\limits_{{n - 1}}^{\infty } {\frac{{f(n)}}{{{n^s}}}} $$ (*) where f is an arithmetical function and s is a real variable, is called a Dirichlet series. It will be called the Dirichlet series of f. There exist Dirichlet series such that for all values of s, the series does not converge absolutely (see Exercise 5.1).
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On the generalized order of dirichlet series
Acta Mathematica Scientia, 2015Abstract By the method of Knopp-Kojima, the generalized order of Dirichlet series is studied and some interesting relations on the maximum modulus, the maximum term and the coefficients of entire function defined by Dirichlet series of slow growth are obtained, which briefly extends some results of paper [1].
Yingying Huo, Yinying Kong
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Overconvergence phenomena for generalized Dirichlet series
1999In this paper we show how a wide class of overconvergence phenomena can be described in terms of infinite order differential operators, and that we can provide a multi-dimensional analog for such phenomena.
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