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.

中文翻译：

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数字和和生成函数

我们将原始运算从算术运算（将基数B的整数加起来）连接到q系列，并生成与分区理论中的乘积类似的乘积生成函数。我们发现数字求和生成函数与“ B -ary” Lambert系列的独特类交织在一起，它们本身具有很好的变换。我们还考虑了数字和Dirichlet级数。