The Distribution of Generalized Sum-of-Digits Functions in Residue Classes Original Research Article

Let Q={Qj}∞j=0 be a strictly increasing sequence of integers with Q0=1 and such that each Qj is a divisor of Qj+1. The sequence Q is a numeration system in the sense that every positive integer n has a unique “base-Q” representation of the form n=∑jgreater-or-equal, slanted0 aj(n) Qj with “digits” aj(n) satisfying 0less-than-or-equals, slantaj(n)