A Stothers–Mason theorem with a difference radical
A Stothers–Mason theorem with a difference radical
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DOI：
10.1007/s00209-020-02604-7
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发表时间：
2020-09
影响因子：
0.8
通讯作者：
K. Ishizaki;R. Korhonen;Nan Li;K. Tohge
中科院分区：
文献类型：
--
作者：
K. Ishizaki;R. Korhonen;Nan Li;K. Tohge
微分学并不是观察多项式方程的唯一方法。本文提出了一种应用差分法估计满足上述方程的多项式a，b，c的根的重数的方法。然后利用多项式根的新概念证明了多项式的一个差分定理。作为应用，给出了差分Fermat和差分Super-Fermat泛函方程多项式解的不存在性的结果。我们还介绍了截断差分第二主要定理，并使用它来考虑这些功能方程的非多项式整解。观察具有多项式或非多项式解的方程，以查看所获得的结果的锐度。
Differential calculus is not a unique way to observe polynomial equations such as. We propose a way of applying difference calculus to estimate multiplicities of the roots of the polynomialsa,bandcsatisfying the equation above. Then a differenceabctheorem for polynomials is proved using a new notion of a radical of a polynomial. Results, for example, on the non-existence of polynomial solutions to difference Fermat and difference Super-Fermat functional equations are given as applications. We also introduce a truncated second main theorem for differences, and use it to consider these functional equations with non-polynomial entire solutions. Equations with polynomial or non-polynomial solutions are observed to see the sharpness of results obtained.