$ \RR łatL $We prove a
conjecture due to Dadush, showing that if $\R^n$ is a lattice such
that $\det(łat') 1$ for all sublattices $łat' łat$, then \
\sum_y łat e^-t^2 \|y\|^2 3/2 \; , \ where $t :=
10(n + 2)$. From this we also derive bounds on the number of short lattice
vectors and on the covering radius.
%0 Journal Article
%1 regev2016reverse
%A Regev, Oded
%A Stephens-Davidowitz, Noah
%D 2016
%K mathematics readings theory
%T A Reverse Minkowski Theorem
%U http://arxiv.org/abs/1611.05979
%X $ \RR łatL $We prove a
conjecture due to Dadush, showing that if $\R^n$ is a lattice such
that $\det(łat') 1$ for all sublattices $łat' łat$, then \
\sum_y łat e^-t^2 \|y\|^2 3/2 \; , \ where $t :=
10(n + 2)$. From this we also derive bounds on the number of short lattice
vectors and on the covering radius.
@article{regev2016reverse,
abstract = {$ \newcommand{\R}{\mathbb{R}} \newcommand{\lat}{\mathcal{L}} $We prove a
conjecture due to Dadush, showing that if $\lat \subset \R^n$ is a lattice such
that $\det(\lat') \ge 1$ for all sublattices $\lat' \subseteq \lat$, then \[
\sum_{\vec y \in \lat} e^{-t^2 \|\vec y\|^2} \le 3/2 \; , \] where $t :=
10(\log n + 2)$. From this we also derive bounds on the number of short lattice
vectors and on the covering radius.},
added-at = {2020-02-20T13:03:34.000+0100},
author = {Regev, Oded and Stephens-Davidowitz, Noah},
biburl = {https://www.bibsonomy.org/bibtex/22acf94c53333074d8135ea1632937b24/kirk86},
description = {[1611.05979] A Reverse Minkowski Theorem},
interhash = {526607f10243e38e3a40f2146f9ac58d},
intrahash = {2acf94c53333074d8135ea1632937b24},
keywords = {mathematics readings theory},
note = {cite arxiv:1611.05979},
timestamp = {2020-02-20T13:03:34.000+0100},
title = {A Reverse Minkowski Theorem},
url = {http://arxiv.org/abs/1611.05979},
year = 2016
}