Abstract:Let Fq be the finite field of q elements, where q = p r is a power of the prime p, and (β1, β2, . . . , βr) be an ordered basis of Fq over Fp. Forwe define the Thue-Morse or sum-of-digits function T (ξ) on Fq byxi.For a given pattern length s with 1 ≤ s ≤ q, a subset A = {α1, . . . , αs} ⊂ Fq, a polynomial f (X) ∈ Fq[X] of degree d and a vector c = (c1, . . . , cs) ∈ F s p we putIn this paper we will see that under some natural conditions, the size of T (c, A, f ) is asymptotically the same for all c and A in … Show more
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