Asymptotics of variance of the lattice point count
Czechoslovak Mathematical Journal (2008)
- Volume: 58, Issue: 3, page 751-758
- ISSN: 0011-4642
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topJanáček, Jiří. "Asymptotics of variance of the lattice point count." Czechoslovak Mathematical Journal 58.3 (2008): 751-758. <http://eudml.org/doc/37866>.
@article{Janáček2008,
abstract = {The variance of the number of lattice points inside the dilated bounded set $rD$ with random position in $\mathbb \{R\}^d$ 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.},
author = {Janáček, Jiří},
journal = {Czechoslovak Mathematical Journal},
keywords = {point lattice; Fourier transform; volume; variance; point lattice; Fourier transform; volume; variance},
language = {eng},
number = {3},
pages = {751-758},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Asymptotics of variance of the lattice point count},
url = {http://eudml.org/doc/37866},
volume = {58},
year = {2008},
}
TY - JOUR
AU - Janáček, Jiří
TI - Asymptotics of variance of the lattice point count
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 3
SP - 751
EP - 758
AB - The variance of the number of lattice points inside the dilated bounded set $rD$ with random position in $\mathbb {R}^d$ 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.
LA - eng
KW - point lattice; Fourier transform; volume; variance; point lattice; Fourier transform; volume; variance
UR - http://eudml.org/doc/37866
ER -
References
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