Discrete limit theorems for the Laplace transform of the Riemann zeta-function
Communications in Mathematics, Tome 13 (2005) no. 1, pp. 19-27

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
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.
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.
Classification : 11M06, 44A10, 60F05
Keywords: Laplace transform; probability measure; Riemann zeta-function; weak convergence
Kačinskaitė, R.; Laurinčikas, A. Discrete limit theorems for the Laplace transform of the Riemann zeta-function. Communications in Mathematics, Tome 13 (2005) no. 1, pp. 19-27. http://geodesic.mathdoc.fr/item/COMIM_2005_13_1_a2/
@article{COMIM_2005_13_1_a2,
     author = {Ka\v{c}inskait\.{e}, R. and Laurin\v{c}ikas, A.},
     title = {Discrete limit theorems for the {Laplace} transform of the {Riemann} zeta-function},
     journal = {Communications in Mathematics},
     pages = {19--27},
     year = {2005},
     volume = {13},
     number = {1},
     mrnumber = {2290415},
     zbl = {1251.11055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2005_13_1_a2/}
}
TY  - JOUR
AU  - Kačinskaitė, R.
AU  - Laurinčikas, A.
TI  - Discrete limit theorems for the Laplace transform of the Riemann zeta-function
JO  - Communications in Mathematics
PY  - 2005
SP  - 19
EP  - 27
VL  - 13
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/COMIM_2005_13_1_a2/
LA  - en
ID  - COMIM_2005_13_1_a2
ER  - 
%0 Journal Article
%A Kačinskaitė, R.
%A Laurinčikas, A.
%T Discrete limit theorems for the Laplace transform of the Riemann zeta-function
%J Communications in Mathematics
%D 2005
%P 19-27
%V 13
%N 1
%U http://geodesic.mathdoc.fr/item/COMIM_2005_13_1_a2/
%G en
%F COMIM_2005_13_1_a2

[1] Atkinson F. V.: The mean value of the Riemann zeta-function. Acta Math., 81 (1949), 353–376. | DOI | MR | Zbl

[2] Billingsley P.: Convergence of Probability Measures. Wiley, New York, 1968. | MR | Zbl

[3] Conway J. B.: Functions of One Complex Variable. Springer-Verlag, New York, 1973. | MR | Zbl

[4] Heyer H.: Probability Measures on Locally Compact Groups. Springer-Verlag, Berlin, 1977. | MR | Zbl

[5] Ivič A.: The Riemann Zeta-Function. Wiley, New York, 1985. | MR

[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

[7] Laurinčikas A.: Limit theorems for the Laplace transform of the Riemann zeta-function. Integral Transf. Special Functions (to appear). | MR