Digit sums and generating functions
arXiv:1807.06710 · doi:10.1007/s11139-019-00193-6
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.
10 pages