Summing the sum of digits
Number Theory
2026-05-27 v3 Discrete Mathematics
Combinatorics
Abstract
We revisit and generalize inequalities for the summatory function of the sum of digits in a given integer base. We prove that several known results can be deduced from a theorem in a 2023 paper by Mohanty, Greenbury, Sarkany, Narayanan, Dingle, Ahnert, and Louis, whose primary scope is the maximum mutational robustness in genotype-phenotype maps.
Keywords
Cite
@article{arxiv.2311.16806,
title = {Summing the sum of digits},
author = {Jean-Paul Allouche and Manon Stipulanti},
journal= {arXiv preprint arXiv:2311.16806},
year = {2026}
}
Comments
10 pages; this is a revised version to appear in Communications in Mathematics