On multiplicative independence of rational function iterates

Marley Young

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arXiv · 1708.00944

On multiplicative independence of rational function iterates

Marley Young

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Abstract

We give lower bounds for the degree of multiplicative combinations of iterates of rational functions (with certain exceptions) over a general field, establishing the multiplicative independence of said iterates. This leads to a generalisation of Gao's method for constructing elements in the finite field $\mathbb{F}_{q^n}$ whose orders are larger than any polynomial in $n$ when $n$ becomes large. Additionally, we discuss the finiteness of polynomials which translate a given finite set of polynomials to become multiplicatively dependent.

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Marley Young. 2017-08-02. On multiplicative independence of rational function iterates. https://arxiv.org/abs/1708.00944

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