An extremal problem for the geometric mean of polynomials

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