Average growth of L p norms of Erdős–Szekeres polynomials

We study the average growth of p th powers of L p noms on the unit circle of Erdős–Szekeres polynomials P_n( { s_j} ,z) = ∏_j=1^n(1-z^s_j) where 1 ≤ s_1,s_2 , … ,s_n≤ M and M,n→∞ . In particular, we show the average growth is geometric and determine the precise geometric growth. We also analyze the variance.