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arXiv · 1711.01507

The $abc$-Conjecture implies uniform bounds on dynamical Zsigmondy sets

Nicole Looper
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Abstract

We prove that the $abc$-Conjecture implies upper bounds on Zsigmondy sets that are uniform over families of unicritical polynomials over number fields. As an application, we use the $abc$-Conjecture to prove that there exist uniform bounds on the index of the associated arboreal Galois representations.

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Nicole Looper. 2017-11-04. The $abc$-Conjecture implies uniform bounds on dynamical Zsigmondy sets. https://arxiv.org/abs/1711.01507

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