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Value distribution of general Dirichlet series. IV. (English. Russian original) Zbl 1067.11056

Lith. Math. J. 43, No. 3, 281-294 (2003); translation from Liet. Mat. Rink 43, No. 3, 342-358 (2003).
General Dirichlet series \(\sum_{m=1}^{\infty} a_m\exp\{-\lambda_m s\}\), where \(s=\sigma+\imath t, a_m\in C, 0<\lambda_1<\lambda_2<\cdots\) with \(\lim_{m\to\infty}\lambda_m=+\infty,\) are considered. Limit theorem in the space of meromorphic functions is proved. The limiting measure is given explicitly.
Part III, cf. A. Laurinčikas, W. Schwarz and J. Steuding, Dubickas, A. (ed.) et al., Analytic and probabilistic methods in number theory. Proceedings of the third international conference in honour of J. Kubilius, Palanga, Lithuania 2001. Vilnius: TEV, 137–156 (2002; Zbl 1195.11118). Part V, see Lith. Math. J. 44, No. 2, 145–156 (2004; Zbl 1065.11070).

MSC:

11M41 Other Dirichlet series and zeta functions
60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
30B50 Dirichlet series, exponential series and other series in one complex variable
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