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Journal of the Ramanujan Mathematical Society

Volume 37, Issue 2, June 2022  pp. 173–183.

On the well distribution of restricted strongly q-additive functions

Authors:  Lobna Ben Mahfoudh
Author institution:Faculty of Science of Sfax, Soukra Road km 3.5, BP 1171, 3000 Sfax, Tunisia

Summary:  Let (u{n}){n ∈ N{0}} be a sequence of real numbers, q an integer ≥ 2, E an infinite subset of N{0}. If f is a strongly q-additive function, we define fE to be the restricted strongly q-additive function derived from f . i.e. for n = ∑{ν}{k = 0} n{k} q{k}, where ∀ k ∈ {0, … , ν}, nk ∈ {0, … , q − 1}, we have f (n) = ∑{ν}{k=0} f (n{k}) and f{E} (n) = ∑{ν}{k=0}{k ∈ E} f (n{k}). The aim of this work is to prove that if (u{n}){n ∈ N{0}} is well distributed mod 1 then (u{fE(n)}){n ∈ N{0}} is also well distributed mod 1.

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