The second-order factorable core of polynomials over finite fields
The authors look at polynomials \(f^*(x,y)= f(x)-f(y)\) where \(f(x)\in \mathbb{F}_q [x]\) over a finite field \(\mathbb{F}_q\). A sample result from the paper is given as follows. Let \(s\in\mathbb{N}\) be the number of quadratic irreducible factors of \(f^*(x,y)\) over the algebraic closure of \(\mathbb{F}_q\), having no \(xy\) term. Then, under a suitable hypothesis, \(f(x-c)=h ((x^2+b)^{s +1})\) for some \(h(x)\in \mathbb{F}_q[x]\), where \(f(x)= aD(x+b)+c\), and \(D(x)\) is a suitable chosen Dickson polynomial.
scientific article; zbMATH DE number 1309606