The Sum-of-Digits Function for Complex Bases
Peter J. Grabner, Peter Kirschenhofer, Helmut Prodinger · Journal of the London Mathematical Society · 1998
We consider digital expansions with respect to complex integer bases. We derive precise information about the length of these expansions and the corresponding sum-of-digits function. Furthermore we give an asymptotic formula for the sum-of-digits function in large circles and prove that this function is uniformly distributed with respect to the argument. Finally the summatory function of the sum-of-digits function along the real axis is analyzed.