- On the formal series Witt transform
- Discrete mathematics
- Volume | Issue number
- 295 | 1-3
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
- Given a formal power series f(z)∈C〚z〛f(z)∈C〚z〛 we define, for any positive integer r, its r th Witt transform, Wf(r), by Wf(r)(z)=1r∑d|rμ(d)f(zd)r/d,
where μμ denotes the Möbius function. The Witt transform generalizes the necklace polynomials, M(α;n)M(α;n), that occur in
the cyclotomic identity
1/1-αy = ∏n=1∞(1-yn)-M(α;n).
Several properties of Wf(r) are established. Some examples relevant to number theory are considered.
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