Integral Matrices of Fixed Rank over Number Fields
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908589762805760 |
|---|---|
| author | Gargava, Nihar Serban, Vlad Viazovska, Maryna Viglino, Ilaria |
| author_facet | Gargava, Nihar Serban, Vlad Viazovska, Maryna Viglino, Ilaria |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11673 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integral Matrices of Fixed Rank over Number Fields Gargava, Nihar Serban, Vlad Viazovska, Maryna Viglino, Ilaria Number Theory Information Theory 11H06, 11H50, 68R01, 94B75 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. |
| title | Integral Matrices of Fixed Rank over Number Fields |
| topic | Number Theory Information Theory 11H06, 11H50, 68R01, 94B75 |
| url | https://arxiv.org/abs/2510.11673 |