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- integer -- to -series and product generating functions analogous to those in partition theory. We find digit sum generating functions to be intertwined with distinctive classes of "-ary" Lambert series, which themselves enjoy nice transformations. We also consider digit sum Dirichlet series.
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