Geodesic
Lattice points in many-dimensional balls
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 32, Tome 449 (2016), pp. 261-274

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

Let $P_k(n)$ be the difference of the number of points of the integer lattice contained in the ball $y_1^2+\dots+y_k^2\leq n$ and the volume of this ball. We investigate the asymptotic behavior of the sums $\sum_{n\leq x}P_k(n)$, $(k\geq4)$, $\sum_{n\leq x}P_3^2(n)$, and $\sum_{n\leq x}P_4^2(n)$ as $x\to+\infty$. 
@article{ZNSL_2016_449_a12,
     author = {O. M. Fomenko},
     title = {Lattice points in many-dimensional balls},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {261--274},
     publisher = {mathdoc},
     volume = {449},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_449_a12/}
}
TY  - JOUR
AU  - O. M. Fomenko
TI  - Lattice points in many-dimensional balls
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2016
SP  - 261
EP  - 274
VL  - 449
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2016_449_a12/
LA  - ru
ID  - ZNSL_2016_449_a12
ER  - 
%0 Journal Article
%A O. M. Fomenko
%T Lattice points in many-dimensional balls
%J Zapiski Nauchnykh Seminarov POMI
%D 2016
%P 261-274
%V 449
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2016_449_a12/
%G ru
%F ZNSL_2016_449_a12
O. M. Fomenko. Lattice points in many-dimensional balls. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 32, Tome 449 (2016), pp. 261-274. http://geodesic.mathdoc.fr/item/ZNSL_2016_449_a12/