Integral Matrices of Fixed Rank over Number Fields
Number Theory
2025-10-14 v1 Information Theory
math.IT
Abstract
We prove an asymptotic formula for the number of fixed rank matrices with integer coefficients over a number field K/Q and bounded norm. As an application, we derive an approximate Rogers integral formula for discrete sets of module lattices obtained from lifts of algebraic codes. This in turn implies that the moment estimates of random lattices with a number field structure also carry through for large enough discrete sets of module lattices.
Keywords
Cite
@article{arxiv.2510.11673,
title = {Integral Matrices of Fixed Rank over Number Fields},
author = {Nihar Gargava and Vlad Serban and Maryna Viazovska and Ilaria Viglino},
journal= {arXiv preprint arXiv:2510.11673},
year = {2025}
}
Comments
Our previous preprint 2402.10305 on this topic is broken into two different parts. This is one of the two parts