Monomial functions, normal polynomials and polynomial equations

Abstract

AbstractIn this paper we consider generalized monomial functions $$f, g:{\mathbb {F}}\rightarrow {\mathbb {C}}$$ f , g : F → C (of possibly different degree) that also fulfill $$\begin{aligned} f(P(x))= Q(g(x)) \qquad \left( x\in {\mathbb {F}}\right) , \end{aligned}$$ f ( P ( x ) ) = Q ( g ( x ) ) x ∈ F , where $$P\in {\mathbb {F}}[x]$$ P ∈ F [ x ] and $$Q\in {\mathbb {C}}[x]$$ Q ∈ C [ x ] are given (classical) polynomials.