Sur les puissances des polynômes sur un corps fini

Abstract : 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.
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Mireille Car, Christian Mauduit. Sur les puissances des polynômes sur un corps fini. Uniform Distribution Theory, Mathematical Institute of the Slovak Academy of Sciences, 2013, 8 (2), pp.171-182. ⟨https://math.boku.ac.at/udt/vol08/no2/vol8nr2.htm⟩. ⟨hal-01272342⟩

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