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arXiv · 1807.06710

Digit sums and generating functions

Maxwell Schneider·Robert Schneider
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Abstract

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

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Maxwell Schneider, Robert Schneider. 2020-06-14. Digit sums and generating functions. https://doi.org/10.1007/s11139-019-00193-6

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