The formal series Witt transform
Abstract
Description
Given a formal power series f(z) we define, for any positive integer r, its rth Witt transform, W_f^{(r)}, by rW_f^{(r)}(z)=sum_{d|r}mu(d)f(z^d)^{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-y^n)^{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.
18 pages, small improvements in contents and presentation, to appear in Discrete Mathematics
18 pages, small improvements in contents and presentation, to appear in Discrete Mathematics