Abstract
The distribution of the vector (|ζ(s, α)|; ζ(s, α)), where ζ(s, α) is the Hurwitz zeta-function with transcendental parameter α, is considered and a probabilistic limit theorem is obtained. Also, the dependence between |ζ(s, α)| and ζ(s, α) in terms of m-characteristic transforms is discussed.
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References
Bagchi B., The Statistical Behaviour and Universality Properties of the Riemann Zeta-Function and Other Allied Dirichlet Series, Ph.D. thesis, Indian Statistical Institute, Calcutta, 1981
Billingsley P., Convergence of Probability Measures, Wiley, New York, 1968
Genys J., Laurinčikas A., Weighted limit theorems for general Dirichlet series, Unif. Distrib. Theory, 2007, 2(2), 49–66
Laurinčikas A., Distribution of values of complex-valued functions, Litovsk. Mat. Sb., 1975, 15(2), 25–39, (in Russian)
Laurinčikas A., Limit Theorems for the Riemann Zeta-Function, Kluwer Academic Publishers, Dordrecht, 1996
Laurinčikas A., Limit theorems for general Dirichlet series, Theory Stoch. Process., 2002, 8(3–4), 256-268
Laurinčikas A., Remarks on characteristic transforms of probability measures, Šiauliai Math. Semin., 2007, 2(10), 43–52
Laurinčikas A., Garunkštis R., The Lerch Zeta-Function, Kluwer, Dordrecht, 2002
Laurinčikas A., Macaitienė R., The characteristic transforms on ℝ×ℂ, Integral Transforms Spec. Funct., 2008, 19(1–2), 11–22
Matsumoto K., Probabilistic value-distribution theory of zeta-functions, Sugaku Expositions, 2004, 17(1), 51–71
Steuding J., Value-Distribution of L-Functions, Lecture Notes in Mathematics, 1877, Springer, Berlin, 2007
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Laurinčikas, A. On limit distribution of the Hurwitz zeta-function. centr.eur.j.math. 8, 786–794 (2010). https://doi.org/10.2478/s11533-010-0043-2
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DOI: https://doi.org/10.2478/s11533-010-0043-2