Theorem
Proof This is equivalent to:
which on substituting 
becomes
The equivalence follows from the identity
Littlewood's Other Conjecture Conjecture (1966) There is some
so that for all z on the boundary of the unit disc
Littlewood, in part, based his conjecture on computations
of
all such polynomials up to degree twenty.
Odlyzko has now done 200 MIPS years of computing
on this problem