Geodesic
Asymptotics of variance of the lattice point count
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 3, pp. 751-758.

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

The variance of the number of lattice points inside the dilated bounded set $rD$ with random position in $\Bbb R^d$ has asymptotics $\sim r^{d-1}$ if the rotational average of the squared modulus of the Fourier transform of the set is $O(\rho ^{-d-1})$. The asymptotics follow from Wiener's Tauberian theorem.
Classification : 11H06, 62D05
Keywords: point lattice; Fourier transform; volume; variance 
@article{CMJ_2008__58_3_a12,
     author = {Jan\'a\v{c}ek, Ji\v{r}{\'\i}},
     title = {Asymptotics of variance of the lattice point count},
     journal = {Czechoslovak Mathematical Journal},
     pages = {751--758},
     publisher = {mathdoc},
     volume = {58},
     number = {3},
     year = {2008},
     mrnumber = {2455936},
     zbl = {1174.60002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2008__58_3_a12/}
}
TY  - JOUR
AU  - Janáček, Jiří
TI  - Asymptotics of variance of the lattice point count
JO  - Czechoslovak Mathematical Journal
PY  - 2008
SP  - 751
EP  - 758
VL  - 58
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_2008__58_3_a12/
LA  - en
ID  - CMJ_2008__58_3_a12
ER  - 
%0 Journal Article
%A Janáček, Jiří
%T Asymptotics of variance of the lattice point count
%J Czechoslovak Mathematical Journal
%D 2008
%P 751-758
%V 58
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_2008__58_3_a12/
%G en
%F CMJ_2008__58_3_a12
Janáček, Jiří. Asymptotics of variance of the lattice point count. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 3, pp. 751-758. http://geodesic.mathdoc.fr/item/CMJ_2008__58_3_a12/