The formal series Witt transform
Combinatorics
2007-05-23 v2 Number Theory
Abstract
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.
Keywords
Cite
@article{arxiv.math/0311194,
title = {The formal series Witt transform},
author = {Pieter Moree},
journal= {arXiv preprint arXiv:math/0311194},
year = {2007}
}
Comments
18 pages, small improvements in contents and presentation, to appear in Discrete Mathematics