The 𝐴𝐵𝐶-Conjecture implies uniform bounds on dynamical Zsigmondy sets

Looper, Nicole

doi:10.1090/tran/8082

The $ABC$-Conjecture implies uniform bounds on dynamical Zsigmondy sets
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by Nicole R. Looper PDF

Trans. Amer. Math. Soc. 373 (2020), 4627-4647 Request permission

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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