Uniform bounds on periodic points of polynomials with good reduction
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915586728001536 |
|---|---|
| author | Rajagopal, Isaac Zhang, Robin |
| author_facet | Rajagopal, Isaac Zhang, Robin |
| contents | We establish effective bounds on the number of periodic points of degree-$d$ polynomials $ϕ$ defined over $p$-adic fields and number fields, under a mild reduction hypothesis that is satisfied by all unicritical polynomials $X^d + c$ with $c$ integral at some prime dividing $d$. As a consequence, we verify the uniform boundedness conjecture for this class of polynomials over number fields $K$, giving the explicit uniform bound $\#\mathrm{Per}_K(ϕ) \leq d^{[K:\mathbb{Q}]}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26119 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniform bounds on periodic points of polynomials with good reduction Rajagopal, Isaac Zhang, Robin Number Theory Dynamical Systems 37P05 (Primary) 11S15, 14G05, 37P15, 37P20 (Secondary) We establish effective bounds on the number of periodic points of degree-$d$ polynomials $ϕ$ defined over $p$-adic fields and number fields, under a mild reduction hypothesis that is satisfied by all unicritical polynomials $X^d + c$ with $c$ integral at some prime dividing $d$. As a consequence, we verify the uniform boundedness conjecture for this class of polynomials over number fields $K$, giving the explicit uniform bound $\#\mathrm{Per}_K(ϕ) \leq d^{[K:\mathbb{Q}]}$. |
| title | Uniform bounds on periodic points of polynomials with good reduction |
| topic | Number Theory Dynamical Systems 37P05 (Primary) 11S15, 14G05, 37P15, 37P20 (Secondary) |
| url | https://arxiv.org/abs/2510.26119 |