J. Doyle

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20112021

most citedPreperiodic points for quadratic polynomials over quadratic fields

12 citations · 38 across the 14 of their papers we have counts for

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Showing 2021 · math.NTShow all

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math.NT2021

Dynatomic polynomials, necklace operators, and universal relations for dynamical units

John R. Doyle, Paul Fili, Trevor Hyde

Given a generic polynomial $f (x)$ , the generalized dynatomic polynomial $Φ_{f, c, d} (x)$ vanishes at precisely those $α$ such that $f^{c} (α)$ has period exactly $d$ under iteration of…

math.NT2021

Galois groups and prime divisors in random quadratic sequences

John R. Doyle, Vivian Olsiewski Healey, Wade Hindes +1

Given a set $S = {x^{2} + c_{1}, \dots, x^{2} + c_{s}}$ defined over a field and an infinite sequence $γ$ of elements of $S$ , one can associate an arboreal representation to $γ$ , generalizing th…