2012/10/27 by Jordan Bell, Bell, Jordan
Mathematics · #26D05 #40A25 #42A05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT) #math.CA #math.NT #msc:26D05 #msc:40A25 #msc:42A05
paper · pdf · doi:10.48550/arxiv.1210.7380
18 pages
arxiv created 2012/10/27 · arxiv updated 2012/10/30
In this paper we prove asymptotic formulas for the Lp norms of Pn(θ)=∏k=1n (1-eikθ) and Qn(θ)=∏k=1n (1+eikθ). These products can be expressed using ∏k=1n sin((kθ)/(2)) and ∏k=1n cos((kθ)/(2)) respectively. We prove an estimate for Pn at a point near where its maximum occurs. Finally, we give an asymptotic formula for the maximum of the Fourier coefficients of Qn.