Exponential sums of sum-of-digit functions
Let \(\beta\) (n) denote the sum of digits of the natural number n represented to base b and let \(q>0\). The author studies the function \(\phi (x)=\sum_{n<x}q^{\beta (n)}\), thereby extending results by \textit{H. Harborth} [Proc. Am. Math. Soc. 62, 19-22 (1977; Zbl 0323.10043)], \textit{K. B. Stolarsky} [SIAM J. Appl. Math. 32, 717-730 (1977; Zbl 0355.10012)] and himself [Proc. Am. Math. Soc. 80, 526-530 (1980; Zbl 0448.10011)].
scientific article; zbMATH DE number 3961736