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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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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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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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General Dirichlet series and Bohr’s equivalence theorem
1976This 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.
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An overview of precision oncology basket and umbrella trials for clinicians
Ca-A Cancer Journal for Clinicians, 2020Kristian Thorlund, Edward J Mills
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Cancer risk among World Trade Center rescue and recovery workers: A review
Ca-A Cancer Journal for Clinicians, 2022Paolo Boffetta +2 more
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An extension of Maass theory to general Dirichlet series
, 2022 Xiaohan Wang +2 more
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