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Keywords:
Laplace transform; probability measure; Riemann zeta-function; weak convergence
Laplace transform; probability measure; Riemann zeta-function; weak convergence
Summary:
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.
References:
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[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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