Somme des chiffres et changement de base

Abstract

For q⩾2, let s q (n) denote the sum of digits of an integer n in the base q expansion. Answering, in an extended form, a question of Deshouillers, Habsieger, Laishram, and Landreau, we show that, provided a and b are multiplicatively independent, any positive real number is a limit point of the sequence {s b (n)/s a (n)} n=1 ∞ . We also provide upper and lower bounds for the counting functions of the corresponding subsequences.

Locations

• arXiv (Cornell University) - View - PDF
• French digital mathematics library (Numdam) - View - PDF
• HAL (Le Centre pour la Communication Scientifique Directe) - View
• Annals of the Fourier Institute (Institut Fourier) - View - PDF
• Annales de l’institut Fourier - View - PDF