English

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

R2 v1 2026-06-28T13:34:10.567Z