Year: 2026
Type: preprint
Abstract: We prove the dynamical uniform boundedness conjecture for unicritical polynomials $z^d + c$ over every number field $K$ when $d \geq 4$, and over every number field $K$ not containing $\mathbb{Q}(\sqrt{-3})$ when $d = 3$. Furthermore, our unconditional bounds on perodic points are effectively computable. In the remaining cases, we show that the dynamical uniform boundedness conjecture is implied by the boundedness of Mordell-Weil ranks over $K$ for a specific family of elliptic curves when $d = 3$ and for Jacobians of dynatomic curves when $d = 2$.
Source: arXiv (Cornell University)
Author: Zhang, Robin
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213313984