Number of characteristic polynomials of matrices with bounded height

Autor:	Mérai, László, Shparlinski, Igor E.
Rok vydání:	2023
Předmět:	Mathematics - Number Theory
Druh dokumentu:	Working Paper
Popis:	We consider the set $\mathcal{M}_n(\mathbb{Z}; H)$ of $n\times n$-matrices with integer elements of size at most $H$ and obtain upper and lower bounds on the number of distinct irreducible characteristic polynomials which correspond to these matrices and thus on the number of distinct eigenvalues of these matrices. In particular, we improve some results of A. Abrams, Z. Landau, J. Pommersheim and N. Srivastava (2022).
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.09052 Zobrazit plný text záznamu View this record from Arxiv