A limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for the Estermann zeta-function is obtained.
@article{bwmeta1.element.doi-10_2478_BF02475619,
author = {Antanas Laurin\v cikas},
title = {Limit theorems for the Estermann zeta-function. II},
journal = {Open Mathematics},
volume = {3},
year = {2005},
pages = {580-590},
zbl = {1122.11058},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475619}
}
Antanas Laurinčikas. Limit theorems for the Estermann zeta-function. II. Open Mathematics, Tome 3 (2005) pp. 580-590. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475619/
[1] P. Billingsley: Convergence of Probbility Measures, Wiley, New York, 1968.
[2] H. Bohr and B. Jessen: “Über die Wertverteilung der Riemannschen Zeta funktion”, Erste Mitteilung, Acta Math., Vol. 54, (1930), pp. 1–35. | Zbl 56.0287.01
[3] H. Bohr and B. Jessen: “Über die Wertverteilung der Riemannschen Zeta funktion”, Zweite Mitteilung, Acta Math., Vol. 58, (1932), pp. 1–55. | Zbl 58.0321.02
[4] J.B. Conway: Functions of One Complex Variable, Springer-Verlag, New York, 1973.
[5] J. Genys and A. Laurinčikas: “Value distribution of general Dirichlet series. IV”, Liet. Matem. Rink, Vol. 43, No. 3, (2003), pp. 342–358; Lith. Math. J., Vol. 42, No. e, (2003), pp. 281–294 (in Russian). | Zbl 1067.11056
[6] A. Laurinčikas: Limit Theorems for the Riemann Zeta-function, Kluwer, Dordrecht, Boston, London, 1996.
[7] A. Laurinčikas and R. Garunkštis: The Lerch Zeta-Function, Kluwer, Dordrecht, Boston, London, 2002. | Zbl 1028.11052
[8] A. Laurinčikas: “Limit theorems for the Estermann zeta-function. I”, Satist. Probab. Letters, Vol. 72(3), (2005), pp. 227–235. http://dx.doi.org/10.1016/j.spl.2004.11.024 | Zbl 1121.11059
[9] M. Loève: Probability Theory, Van Nostrand, Toronto, 1955.