Lengths, periods and expansions of elements written with respect to a digit system over

Let , and . For , the expansion f=∑di(x)yi is called a y-adic expansion. Scheicher and Thuswaldner characterized those p(x,y) which render finite and periodic y-adic expansions. Here bounds on the lengths of elements whose expansions are finite, on the periods of elements with periodic expansions, conditions for a periodic expansion to have a prescribed period are determined and certain elements with infinite, non-periodic expansions are investigated.