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Module lattices and their shortest vectors
October 14, 2025 · Declared Dead · 🏛 arXiv.org
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Authors
Nihar Gargava, Vlad Serban, Maryna Viazovska, Ilaria Viglino
arXiv ID
2510.12893
Category
math.NT
Cross-listed
cs.IT
Citations
1
Venue
arXiv.org
Last Checked
1 month ago
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.
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