A lower bound on the canonical height for polynomials

TL;DR

This paper establishes a fundamental lower bound on the canonical height for polynomials over number fields, depending on degree, field degree, and bad reduction places, advancing understanding of polynomial dynamics.

Contribution

It provides the first explicit lower bound on canonical heights for polynomials over number fields based on key invariants.

Findings

Lower bound depends only on polynomial degree, field degree, and bad reduction places.

The bound applies to points with infinite forward orbit.

Enhances understanding of polynomial dynamics over number fields.

Abstract

We prove a lower bound on the canonical height associated to polynomials over number fields evaluated at points with infinite forward orbit. The lower bound depends only on the degree of the polynomial, the degree of the number field, and the number of places of bad reduction.