Results 211 to 220 of about 15,056,914 (247)

Value Distribution of General Dirichlet Series. V

Lithuanian Mathematical Journal, 2004
Let \(s\) be a complex variable; then the series \(f_j(s)=\sum_{m=1}^\infty a_{mj}\exp(-s\lambda_m)\) is called a general Dirichlet series. In the present paper, the authors prove a joint universality theorem (in the sense of Voronin) for a family of general Dirichlet series \(f_j(s)\) subject to certain, mostly natural, conditions on the arithmetic of
Genys, J., Laurinčikas, A.
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On the generalized order of dirichlet series

Acta Mathematica Scientia, 2015
Abstract 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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The universality of general Dirichlet series

Analysis, 2003
The 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, Schwarz, Wolfgang, Steuding, Jörn   +2 more
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Absolute convergence of general multiple dirichlet series

Research in Number Theory, 2023
In 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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REPRESENTATION OF FUNCTIONS BY GENERALIZED DIRICHLET SERIES

Russian Mathematical Surveys, 1969
This 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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Joint universality of general Dirichlet series

Izvestiya: Mathematics, 2005
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A Joint Limit Theorem for General Dirichlet Series

Lithuanian Mathematical Journal, 2004
Let be given a collection of Dirichlet series \((s)=\sum_{m=1}^\infty a_{mj} e^{-\lambda_{mj}s}\) where \({mj}\) and \(\lambda_{mj}\) are real, \(\lambda_{mj}>C_j(\log m)^{\theta_j}\) for some \(\theta_j\). It is shown that if \(\lambda_{jm}\) are linearly independent over the field of rational numbers, then the measure \((A)={1\over T}\text{meas ...
Genys, J., Laurinčikas, A.
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The generalized lower order of Dirichlet series

Acta Mathematica Scientia, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Qingyuan, Huo, Yingying
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Dirichlet Series and Generating Functions

1986
A 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 general and random Dirichlet series and their partial sums

Analysis Mathematica
This paper is concerned with the convergence of random Dirichlet series \(S(t)=\sum_{k=1}^\infty \varepsilon_k a_k e^{i\lambda_k t}\), where \((\varepsilon_k)_{k\ge 1}\) is a Rademacher sequence, \((a_k)_{k\ge 1}\) a given sequence of complex numbers, and \(0\le \lambda_1 < \lambda_2 < \cdots\), \(\lambda_k \rightarrow +\infty\).
Konyagin, S., Queffélec, H.
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