Module lattices and their shortest vectors
Number Theory
2025-10-16 v1 Information Theory
math.IT
Abstract
We study the shortest vector lengths in module lattices over arbitrary number fields, with an emphasis on cyclotomic fields. In particular, we sharpen the techniques of arXiv:2308.15275v2 to establish improved results for the variance of the number of lattice vectors of bounded Euclidean norm in a random module lattice. We then derive tight probabilistic bounds for the shortest vector lengths for several notions of random module lattice.
Cite
@article{arxiv.2510.12893,
title = {Module lattices and their shortest vectors},
author = {Nihar Gargava and Vlad Serban and Maryna Viazovska and Ilaria Viglino},
journal= {arXiv preprint arXiv:2510.12893},
year = {2025}
}
Comments
20 pages. This article is an improved and augmented version of some of the results in arXiv:2402.10305