Bounds on Autocorrelation Coefficients of Rudin-Shapiro Polynomials

Abstract

We study the autocorrelation coefficients of the Rudin-Shapiro polynomials, proving in particular that their maximum on the interval $[1,2^n)$ is bounded from below by $C_1{2}^{\alpha n}$ and is bounded from above by $C_2{2}^{{\alpha }^{\prime }n}$ where $\alpha =\mathrm{0.7302852...}$ and ${\alpha }^{\prime }=\mathrm{0.7302867...}$.