Geodesic
The analogue of the law of large numbers for additive functions on sparse sets
Matematičeskie zametki, Tome 18 (1975) no. 5, pp. 687-698

Voir la notice de l'article provenant de la source Math-Net.Ru

An analog of the Turan'n–Kubilyus inequality is proved for a sufficiently wide class of sequences which contains, in particular, $a_n=f(n)$ and $a_n=f(p_n)$, where $f(n)$ is a polynomial with integral coefficients. This result helps us to obtain integral limit theorems for additive functions on the class of sequences under investigation. 
@article{MZM_1975_18_5_a4,
     author = {B. V. Levin and N. M. Timofeev},
     title = {The analogue of the law of large numbers for additive functions on sparse sets},
     journal = {Matemati\v{c}eskie zametki},
     pages = {687--698},
     publisher = {mathdoc},
     volume = {18},
     number = {5},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_5_a4/}
}
TY  - JOUR
AU  - B. V. Levin
AU  - N. M. Timofeev
TI  - The analogue of the law of large numbers for additive functions on sparse sets
JO  - Matematičeskie zametki
PY  - 1975
SP  - 687
EP  - 698
VL  - 18
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1975_18_5_a4/
LA  - ru
ID  - MZM_1975_18_5_a4
ER  - 
%0 Journal Article
%A B. V. Levin
%A N. M. Timofeev
%T The analogue of the law of large numbers for additive functions on sparse sets
%J Matematičeskie zametki
%D 1975
%P 687-698
%V 18
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1975_18_5_a4/
%G ru
%F MZM_1975_18_5_a4
B. V. Levin; N. M. Timofeev. The analogue of the law of large numbers for additive functions on sparse sets. Matematičeskie zametki, Tome 18 (1975) no. 5, pp. 687-698. http://geodesic.mathdoc.fr/item/MZM_1975_18_5_a4/