Mason's theorem with a difference radical

2018/06/01 by Ishizaki, Katsuya, Korhonen, Risto, Li, Nan +1
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.00209

Abstract

Differential calculus is not a unique way to observe polynomial equations such as a+b=c. We propose a way of applying difference calculus to estimate multiplicities of the roots of the polynomials a, b and c satisfying the equation above. Then a difference abc theorem for polynomials is proved using a new notion of a radical of a polynomial. Two results on the non-existence of polynomial solutions to difference Fermat type functional equations are given as applications. We also introduce a truncated second main theorem for differences, and use it to consider difference Fermat type equations with transcendental entire solutions.

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