Estimates for the norms of products of sines and cosines

In this paper we prove asymptotic formulas for the L p norms of P n ( θ ) = ∏ k = 1 n ( 1 − e i k θ ) and Q n ( θ ) = ∏ k = 1 n ( 1 + e i k θ ) . These products can be expressed using ∏ k = 1 n sin ( k θ 2 ) and ∏ k = 1 n cos ( k θ 2 ) respectively. We prove an estimate for P n at a point near where its maximum occurs. Finally, we give an asymptotic formula for the maximum of the Fourier coefficients of Q n .