Results 191 to 200 of about 5,333 (218)

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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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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Overconvergence phenomena for generalized Dirichlet series

1999
In 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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On the value distribution of general Dirichlet series

Annales Polonici Mathematici
Summary: We estimate the number of zeros and poles of \(L-\alpha\), where \(L\) is a general Dirichlet series satisfying some conditions and \(\alpha\) is a meromorphic function with \(T(r,\alpha)=o(r)\) as \(r\rightarrow \infty\). In addition, we give a uniqueness theorem in terms of \(a\)-points of Dirichlet series and find Picard exceptional values ...
Lü, Feng, Cao, Zhi, Lü, Weiran
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A two-variable Dirichlet series and its applications

Quaestiones Mathematicae, 2021
Mehmet Cenkci
exaly  

A Study of the Growth Results for the Hadamard Product of Several Dirichlet Series with Different Growth Indices

Mathematics, 2022
Guang-Sheng Chen, Hong Yan Xu, Hari M Srivastava   +2 more
exaly  

Hardy Spaces of Dirichlet Series and Their Composition Operators

Monatshefte Fur Mathematik, 2002
Frédéric Bayart
exaly  

Isometries between spaces of multiple Dirichlet series

Journal of Mathematical Analysis and Applications, 2019
Manuel Maestre, Jaime Castillo-Medina, Domingo Garcia   +2 more
exaly  

Convergence tests on constant Dirichlet series

Computers and Mathematics With Applications, 2011
Jiajin Wen, Tianyong Han, Chaobang Gao   +2 more
exaly