can have multiple zeros.
If 
is a d-th root of unity,
then 
is a zero of
and therefore a zero of 
for any k such that d | k-1.
Hence it is a zero of multiplicity 2 for 
, a polynomial in P.
Higher multiplicities can be obtained by iterating this procedure.
On the other hand, we do not know whether any 
that is not a root of unity can be a multiple root of any 
.
There do exist power series with coefficients 0,1 that have double
zeros z with |z| <1,
as will be shown in Section 3.
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