Let
M
0
,
n
{M_{0,n}}
be the maximum of the geometric mean of all
n
n
th degree polynomials
∑
n
a
k
e
i
k
t
{\sum ^n}{a_k}{e^{ikt}}
which satisfy
|
a
k
|
=
1
,
k
=
0
,
1
,
⋯
,
n
|{a_k}| = 1,k = 0,1, \cdots ,n
. We show the existence of certain polynomials
R
n
{R_n}
whose geometric mean is asymptotic to
√
n
\surd n
, thus proving that
M
0
,
n
{M_{0,n}}
is itself asymptotic to
√
n
\surd n
.