Examples of Quadratic Polynomials over $\mathbb{Q}$ with Surjective Arboreal Galois Representations

Luck Henderson; Jamie Juul; Brenner Lattin; Enrique Mercado; Mia Schaefer

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arXiv · 2603.25899

Examples of Quadratic Polynomials over $\mathbb{Q}$ with Surjective Arboreal Galois Representations

Luck Henderson·Jamie Juul·Brenner Lattin·Enrique Mercado·Mia Schaefer

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Abstract

We explore families of pairs of quadratic polynomials $f(x)=x^2+c\in \mathbb{Q}$ and $a\in \mathbb{Q}$ with $a$ being a strictly preperiodic point of $f$ to provide infinitely many new examples for which the associated arboreal Galois representations are surjective.

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Luck Henderson, Jamie Juul, Brenner Lattin, Enrique Mercado, Mia Schaefer. 2026-03-26. Examples of Quadratic Polynomials over $\mathbb{Q}$ with Surjective Arboreal Galois Representations. https://arxiv.org/abs/2603.25899

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