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

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

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

Number Theory 2026-03-30 v1

Authors: Luck Henderson , Jamie Juul , Brenner Lattin , Enrique Mercado , Mia Schaefer

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.

Keywords

quadratic polynomials arboreal Galois representations surjective preperiodic points rational numbers

Cite

@article{arxiv.2603.25899,
  title  = {Examples of Quadratic Polynomials over $\mathbb{Q}$ with Surjective Arboreal Galois Representations},
  author = {Luck Henderson and Jamie Juul and Brenner Lattin and Enrique Mercado and Mia Schaefer},
  journal= {arXiv preprint arXiv:2603.25899},
  year   = {2026}
}

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10 pages

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

Abstract

Keywords

Cite

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