English

Digit sums and generating functions

Number Theory 2020-06-16 v4 Combinatorics

Abstract

We connect a primitive operation from arithmetic -- summing the digits of a base-BB integer -- to qq-series and product generating functions analogous to those in partition theory. We find digit sum generating functions to be intertwined with distinctive classes of "BB-ary" Lambert series, which themselves enjoy nice transformations. We also consider digit sum Dirichlet series.

Keywords

Cite

@article{arxiv.1807.06710,
  title  = {Digit sums and generating functions},
  author = {Maxwell Schneider and Robert Schneider},
  journal= {arXiv preprint arXiv:1807.06710},
  year   = {2020}
}

Comments

10 pages

R2 v1 2026-06-23T03:05:10.274Z