تقرير
Irreducibility of polynomials defining parabolic parameters of period 3
| العنوان: | Irreducibility of polynomials defining parabolic parameters of period 3 |
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| المؤلفون: | Koizumi, Junnosuke, Murakami, Yuya, Sano, Kaoru, Takehira, Kohei |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, Mathematics - Dynamical Systems, 11R04, 37P15, 37P35, 11R21 |
| الوصف: | 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 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2408.04850 |
| رقم الأكسشن: | edsarx.2408.04850 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |