有限域上的稳定多项式
Stable Polynomials over Finite Fields
摘要：
利用多项式的结式理论研究了有限域上任意多项式的稳定性，即其所有迭代都不可约的性质。这一结果部分地推广了R. Jones和N.波士顿此外，对于特征三，我们证明了某些三次多项式是不稳定的。我们还利用乘性特征和的Weil界估计了特征为奇的有限域上稳定的任意多项式的个数。
英文摘要：
We use the theory of resultants of polynomials to study the stability of an arbitrary polynomial over a finite field, that is, the property of having all its iterates irreducible. This result partially generalises the quadratic polynomial case described by R. Jones and N. Boston. Moreover, for characteristic three, we show that certain polynomials of degree three are not stable. We also use the Weil bound for multiplicative character sums to estimate the number of stable arbitrary polynomials over finite fields of odd characteristic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
