%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 }