Lower Bounds for the Canonical Height of a Unicritical Polynomial and Capacity
| Autor: | Habegger, Philipp, Schmidt, Harry |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | In a recent breakthrough, Dimitrov solved the Schinzel-Zassenhaus Conjecture. We follow his approach and adapt it to certain dynamical systems arising from polynomials of the form $T^p+c$ where $p$ is a prime number and where the orbit of $0$ is finite. For example, if $p=2$, and $0$ is periodic under $T^2+c$ with $c\in\mathbb{R}\smallsetminus\{-2\}$, we prove a lower bound for the local canonical height of a wandering algebraic integer that is inversely proportional to the field degree. From this we are able to deduce a lower bound for the canonical height of a wandering point that decays like the inverse square of the field degree. Comment: Comments welcome |
| Databáze: | arXiv |
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