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arXiv · 1609.03398

Dynamical Galois groups of trinomials and Odoni's conjecture

Nicole R. Looper
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Abstract

We prove Odoni's conjecture in all prime degrees; namely, we prove that for every positive prime $p$, there exists a degree $p$ polynomial $\varphi\in\mathbb{Z}[x]$ with surjective arboreal Galois representation. We also show that Vojta's conjecture implies the existence of such a polynomial in many degrees $d$ which are not prime.

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BibTeXRIS

Nicole R. Looper. 2016-09-12. Dynamical Galois groups of trinomials and Odoni's conjecture. https://doi.org/10.1112/blms.12227

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