The formal series Witt transform

Given a formal power series f(z)@[email protected][email protected]? we define, for any positive integer r, its rth Witt transform, W"f^(^r^), by W"f^(^r^)(z)[email protected]?"d"|"[email protected](d)f(z^d)^r^/^d, where @m denotes the Mobius function. The Witt transform generalizes the necklace polynomials, M(@a;n), that occur in the cyclotomic [email protected][email protected]?n=1~(1-y^n)^-^M^(^@a^;^n^).Several properties of W"f^(^r^) are established. Some examples relevant to number theory are considered.

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