Geodesic
Lattice point problem and the question of estimation and detection of smooth functions of many variables
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 21, Tome 431 (2014), pp. 198-208

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

We consider the problem of asymptotics of $N_d(m)$, where $N_d(m)$ is the number of integer lattice points in the $d$-dimensional ball of radius $m$ (in $l_1$ and $l_2$-norms) for $d\to\infty$, $m\to\infty$. We show that this asymptotics differs from the asymptotic volume of $d$-dimensional ball of radius $m$ when the rate of convergence of $d$ to infinity is sufficiently high in comparison with that of $m$. 
@article{ZNSL_2014_431_a12,
     author = {I. A. Suslina},
     title = {Lattice point problem and the question of estimation and detection of smooth functions of many variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {198--208},
     publisher = {mathdoc},
     volume = {431},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a12/}
}
TY  - JOUR
AU  - I. A. Suslina
TI  - Lattice point problem and the question of estimation and detection of smooth functions of many variables
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2014
SP  - 198
EP  - 208
VL  - 431
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a12/
LA  - ru
ID  - ZNSL_2014_431_a12
ER  - 
%0 Journal Article
%A I. A. Suslina
%T Lattice point problem and the question of estimation and detection of smooth functions of many variables
%J Zapiski Nauchnykh Seminarov POMI
%D 2014
%P 198-208
%V 431
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a12/
%G ru
%F ZNSL_2014_431_a12
I. A. Suslina. Lattice point problem and the question of estimation and detection of smooth functions of many variables. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 21, Tome 431 (2014), pp. 198-208. http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a12/