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Generalized multiple Dirichlet series and generalized multiple polylogarithms

Generalized multiple Dirichlet series and generalized multiple polylogarithms
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General properties of Dirichlet series

, 2013
For 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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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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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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Joint universality of general Dirichlet series

Izvestiya: Mathematics, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Banach spaces of general Dirichlet series

Journal of Mathematical Analysis and Applications, 2018
Fix a strictly increasing sequence \(\lambda = (\lambda_n)\) of positive real numbers which tends to infinity. The authors study general Dirichlet series of the form \(D=\sum a_n \lambda_n^s\), where the coefficients \((a_n)\) form a sequence of complex numbers, and \(s\) is a complex variable. Denote by \(\mathcal{H}_\infty(\lambda)\) the space of all
CHOI, YUN SUNG, KIM, UN YOUNG, MAESTRE, MANUEL   +2 more
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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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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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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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