General dirichlet series - Open Access .click

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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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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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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dirichlet series
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weak convergence

probability measure
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mathematics - number theory
hardy spaces