Irreducibility of polynomials defining parabolic parameters of period 3
| Autor: | Koizumi, Junnosuke, Murakami, Yuya, Sano, Kaoru, Takehira, Kohei |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Morton and Vivaldi defined the polynomials whose roots are parabolic parameters for a one-parameter family of polynomial maps. We call these polynomials delta factors. They conjectured that delta factors are irreducible for the family $z\mapsto z^2+c$. One can easily show the irreducibility for periods $1$ and $2$ by reducing it to the irreducibility of cyclotomic polynomials. However, for periods $3$ and beyond, this becomes a challenging problem. This paper proves the irreducibility of delta factors for the period $3$ and demonstrates the existence of infinitely many irreducible delta factors for periods greater than $3$. Comment: 12 pages, 4 figures, 2 tables |
| Databáze: | arXiv |
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