Unlikely intersections over finite fields: polynomial orbits in small subgroups

László Mérai; Igor E. Shparlinski

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arXiv · 1904.12621

Unlikely intersections over finite fields: polynomial orbits in small subgroups

László Mérai·Igor E. Shparlinski

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Abstract

We estimate the frequency of polynomial iterations which falls in a given multiplicative subgroup of a finite field of $p$ elements. We also give a lower bound on the size of the subgroup which is multiplicatively generated by the first $N$ elements in an orbit. We derive these from more general results about sequences of compositions or a fixed set of polynomials.

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László Mérai, Igor E. Shparlinski. 2019-09-11. Unlikely intersections over finite fields: polynomial orbits in small subgroups. https://arxiv.org/abs/1904.12621

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