Dynamical Galois groups of trinomials and Odoni's conjecture

Nicole R. Looper

doi:10.1112/blms.12227

Dynamical Galois groups of trinomials and Odoni's conjecture

Number Theory 2018-12-19 v2

Authors: 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.

Keywords

Odoni's conjecture arboreal Galois representation dynamical Galois groups trinomials Vojta's conjecture

Cite

@article{arxiv.1609.03398,
  title  = {Dynamical Galois groups of trinomials and Odoni's conjecture},
  author = {Nicole R. Looper},
  journal= {arXiv preprint arXiv:1609.03398},
  year   = {2018}
}

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