Abstract
The present paper deals with functions acting only on the digits of an q-ary expansion. In particular, let n be a positive integer, then we denote by [Formula: see text] its q-ary expansion. We call a function f strictly q-additive if it acts only on the digits of a representation, i.e. [Formula: see text] The goal is to prove that if p is a polynomial having at least one coefficient with bounded continued fraction expansion, then [Formula: see text] This result is motivated by the asymptotic distribution result of Bassily and Kátai and a similar result of Peter.
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