an:07094881
Zbl 07094881
Looper, Nicole
Dynamical Galois groups of trinomials and Odoni's conjecture
EN
Bull. Lond. Math. Soc. 51, No. 2, 278-292 (2019).
00432446
2019
j
11R32 37P15 14G05 11D45
Summary: We prove that for every prime \(p\), there exists a degree \(p\) polynomial whose arboreal Galois representation is surjective, that is, whose iterates have Galois groups over \(\mathbb{Q}\) that are as large as possible subject to a natural constraint coming from iteration. This resolves in the case of prime degree a conjecture of Odoni from 1985. We also show that a standard height uniformity conjecture in arithmetic geometry implies the existence of such a polynomial in many degrees \(d\) which are not prime.