Geodesic
Estimates for the number of rational points on convex curves and surfaces
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XV, Tome 344 (2007), pp. 174-189

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

Let $\Gamma\subset \mathbb R^d$ be a bounded strictly convex surface. Denote by $k_n(\Gamma)$ the number of points in the set $\Gamma\cap\frac1n\mathbb Z^d$. We prove that $\liminf k_n(\Gamma)/n^{d-2}\infty$ for $d\ge 3$ and $\liminf k_n(\Gamma)/\log n\infty$ for $d=2$. 
@article{ZNSL_2007_344_a3,
     author = {F. V. Petrov},
     title = {Estimates for the number of rational points on convex curves and surfaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {174--189},
     publisher = {mathdoc},
     volume = {344},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_344_a3/}
}
TY  - JOUR
AU  - F. V. Petrov
TI  - Estimates for the number of rational points on convex curves and surfaces
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2007
SP  - 174
EP  - 189
VL  - 344
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2007_344_a3/
LA  - ru
ID  - ZNSL_2007_344_a3
ER  - 
%0 Journal Article
%A F. V. Petrov
%T Estimates for the number of rational points on convex curves and surfaces
%J Zapiski Nauchnykh Seminarov POMI
%D 2007
%P 174-189
%V 344
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2007_344_a3/
%G ru
%F ZNSL_2007_344_a3
F. V. Petrov. Estimates for the number of rational points on convex curves and surfaces. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XV, Tome 344 (2007), pp. 174-189. http://geodesic.mathdoc.fr/item/ZNSL_2007_344_a3/