Sur les puissances des polynômes sur un corps fini

Let F a finite field, Q a given element of F[T] with positive degree and k a positive integer. The goal of this work is to study the Q-automaticity of the set of kth powers of elements of F[T] and to calculate the number of polynomials X ∈ F[T] of degree N such that the sum of digits of Xk in base Q is fixed.