定义周期3抛物参数的不可约多项式
Irreducibility of polynomials defining parabolic parameters of period 3
AI总结：
本文证明了周期3的delta因子不可约，并展示了周期大于3时存在无穷多个不可约delta因子，解决了Morton和Vivaldi猜想在周期3的情形。
摘要：
Morton和Vivaldi定义了多项式，其根是单参数多项式族中的抛物参数。我们称这些多项式为delta因子。他们猜想对于族$z\mapsto z^2+c$，delta因子是不可约的。通过将其归结为分圆多项式的不可约性，可以容易地证明周期1和2的不可约性。然而，对于周期3及更高周期，这成为一个具有挑战性的问题。本文证明了周期3的delta因子的不可约性，并展示了对于大于3的周期，存在无穷多个不可约的delta因子。
英文摘要：
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 $3$.
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