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Overconvergence Phenomena For Generalized Dirichlet Series
Overconvergence Phenomena For Generalized Dirichlet Seriesopenaire
Generalized multiple Dirichlet series and generalized multiple polylogarithms
Generalized multiple Dirichlet series and generalized multiple polylogarithmsopenaire
General Properties of Dirichlet Series
, 2020 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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Discrete Limit Theorems for General Dirichlet Series. II
Lithuanian Mathematical Journal, 2004 A 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 \(\{
Renata Macaitienė
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General Dirichlet series and Bohr’s equivalence theorem
, 1990 This chapter treats a class of series, called general Dirichlet series, which includes both power series and ordinary Dirichlet series as special cases. Most of the chapter is devoted to a method developed by Harald Bohr [6] in 1919 for studying the set of values taken by Dirichlet series in a half-plane.
Tom M. Apostol
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Value Distribution of General Dirichlet Series. V
Lithuanian Mathematical Journal, 2004Let \(s\) 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, 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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