The formal series Witt transform
Abstract
Given a formal power series f(z) we define, for any positive integer r, its rth Witt transform, Wf(r), by rWf(r)(z)=sumd|rmu(d)f(zd)r/d, where mu is the Moebius function. The Witt transform generalizes the necklace polynomials M(a,n) that occur in the cyclotomic identity 1-ay=prod (1-yn)M(a,n), where the product is over all positive integers. Several properties of the Witt transform are established. Some examples relevant to number theory are considered.
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