# 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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