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 $\alpha' = 0.7302867...$.

中文翻译：

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Rudin-Shapiro 多项式的自相关系数的界限

我们研究了 Rudin-Shapiro 多项式的自相关系数，特别证明了它们在区间 $[1, 2^n)$ 上的最大值从下限为 $C_1 2^{\alpha n}$ 并且从上限通过 $C_2 2^{\alpha' n}$ 其中 $\alpha = 0.7302852...$ 和 $\alpha' = 0.7302867...$。