Littlewood Polynomials with Small $L^4$ Norm

Jonathan Jedwab, Daniel J. Katz, Kai-Uwe Schmidt

Littlewood asked how small the ratio $||f|{|}_4/||f|{|}_2$ (where $||.|{|}_{\alpha }$ denotes the $L^{\alpha }$ norm on the unit circle) can be for polynomials $f$ having all coefficients in $\{1,-1\}$,…