Number of characteristic polynomials of matrices with bounded height
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912232439283712 |
|---|---|
| author | Mérai, László Shparlinski, Igor E. |
| author_facet | Mérai, László Shparlinski, Igor E. |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_09052 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Number of characteristic polynomials of matrices with bounded height Mérai, László Shparlinski, Igor E. Number Theory 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). |
| title | Number of characteristic polynomials of matrices with bounded height |
| topic | Number Theory |
| url | https://arxiv.org/abs/2310.09052 |