Prime specialization and iterates of composition of Polynomials
Prime specialization and iterates of composition of Polynomials
Given $F(t,x) \in \F_q[t][x]$ a monic, irreducible, separable polynomial of degree $n>0$ in $x$, and a generic monic polynomial $g(\mathbf{a},t)$ of degree $d>1$ in $t$ consisting of algebraically independent coefficients, $(\mathbf{a} )$, taking values in $\F_q$, we establish the standard result, Galois group of the composition of polynomials $F(t,g(\mathbf{a},t))$ over …