有理矩阵的秩、行列式与特征多项式的统计
数论
2026-03-04 v3
摘要
我们考虑分子和分母大小不超过的有理数矩阵集合，得到了给定秩的此类矩阵数量的上下界，并将其应用于计数给定行列式或给定特征多项式的此类矩阵。
引用
@article{arxiv.2401.10086,
title = {Statistics of ranks, determinants and characteristic polynomials of rational matrices},
author = {Muhammad Afifurrahman and Vivian Kuperberg and Alina Ostafe and Igor E. Shparlinski},
journal= {arXiv preprint arXiv:2401.10086},
year = {2026}
}
备注
his is a slight revision of the published version (Forum Math. 2025; v.37, 1259-1289), in which the main and error terms in Theorem 2.6 and Lemma 3.10 all contain an extra factor of $\log H$. The authors are grateful to Nick Rome for noticing this