Sur les fonctions q-additives ou q-multiplicatives

On the counting function for the Niven numbers

“…Theorem 1 will follow from our results on the local distribution of α(n), the sum of the digits of n, when n runs over an arithmetic progression with growing modulus k. Similar techniques for the study of the sum of digits function residue classes have been used by other authors, namely Delange [4] and Gel'fond [6].…”

The joint distribution of Q-additive functions on polynomials over finite fields

“…g-additive functions have been extensively discussed in the literature, in particular their asymptotic distribution, see [1,3,4,5,6,7,8,9,11,12,14,15]. We cite three of these results (in a slightly modified form).…”

The joint distribution of q-additive functions

“…There also exist distributional results for q-additive functions. In 1972 Delange [4] proved an analogue to the Erdős-Wintner theorem. There exists a distribution function F (y) such that, as x → ∞,…”