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Integral Matrices of Fixed Rank over Number Fields
October 13, 2025 · Declared Dead · 🏛 arXiv.org
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Authors
Nihar Gargava, Vlad Serban, Maryna Viazovska, Ilaria Viglino
arXiv ID
2510.11673
Category
math.NT
Cross-listed
cs.IT
Citations
1
Venue
arXiv.org
Last Checked
1 month ago
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.
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