Examples of Quadratic Polynomials over $\mathbb{Q}$ with Surjective Arboreal Galois Representations
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914425902989312 |
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| author | Henderson, Luck Juul, Jamie Lattin, Brenner Mercado, Enrique Schaefer, Mia |
| author_facet | Henderson, Luck Juul, Jamie Lattin, Brenner Mercado, Enrique Schaefer, Mia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25899 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Examples of Quadratic Polynomials over $\mathbb{Q}$ with Surjective Arboreal Galois Representations Henderson, Luck Juul, Jamie Lattin, Brenner Mercado, Enrique Schaefer, Mia Number Theory 37P05 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. |
| title | Examples of Quadratic Polynomials over $\mathbb{Q}$ with Surjective Arboreal Galois Representations |
| topic | Number Theory 37P05 |
| url | https://arxiv.org/abs/2603.25899 |