Estimates for the norms of products of sines and cosines

In this paper we prove asymptotic formulas for the LpLp norms of Pn(θ)=∏k=1n(1−eikθ) and Qn(θ)=∏k=1n(1+eikθ). These products can be expressed using ∏k=1nsin(kθ2) and ∏k=1ncos(kθ2) respectively. We prove an estimate for PnPn at a point near where its maximum occurs. Finally, we give an asymptotic formula for the maximum of the Fourier coefficients of QnQn.