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Laplace transform; probability measure; Riemann zeta-function; weak convergence
In the paper discrete limit theorems in the sense of weak convergence of probability measures on the complex plane as well as in the space of analytic functions for the Laplace transform of the Riemann zeta-function are proved.
[1] Atkinson F. V.: The mean value of the Riemann zeta-function. Acta Math., 81 (1949), 353–376. DOI 10.1007/BF02395027 | MR 0031963 | Zbl 0036.18603
[2] Billingsley P.: Convergence of Probability Measures. Wiley, New York, 1968. MR 0233396 | Zbl 0172.21201
[3] Conway J. B.: Functions of One Complex Variable. Springer-Verlag, New York, 1973. MR 0447532 | Zbl 0277.30001
[4] Heyer H.: Probability Measures on Locally Compact Groups. Springer-Verlag, Berlin, 1977. MR 0501241 | Zbl 0376.60002
[5] Ivič A.: The Riemann Zeta-Function. Wiley, New York, 1985. MR 0792089
[6] Jutila M.: Atkinson’s formula revisited. in: Voronoi’s Impact in Modern Science, Book 1, Proc. Inst. Math. National Acad. Sc. Ukraine, Vol. 21, P. Engel and H. Syta (Eds), Inst. Math., Kyiv, 1998, pp. 137–154. Zbl 0948.11032
[7] Laurinčikas A.: Limit theorems for the Laplace transform of the Riemann zeta-function. Integral Transf. Special Functions (to appear). MR 2242414
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