Bounds on Autocorrelation Coefficients of Rudin-Shapiro Polynomials

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 $C_2 2^{\alpha’ n}$where$\alpha = 0.7302852…$and$\alpha’ = 0.7302867…$.