In signal processing the Rudin–Shapiro polynomials have good autocorrelation properties and their values on the unit circle are small. Binary sequences with low autocorrelation coefficients are of interest in radar, sonar, and communication systems. In this paper we show that the Mahler measure of the Rudin–Shapiro polynomials of degree n − 1 with n = 2^k is asymptotically (2n/e)^1/2, as it was conjectured by B. Saffari in 1985. Our approach is based heavily on the Saffari and Montgomery conjectures proved recently by B. Rodgers.

中文翻译：

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Rudin-Shapiro多项式的Mahler测度的渐近值

在信号处理中，Rudin–Shapiro多项式具有良好的自相关特性，并且它们在单位圆上的值很小。具有低自相关系数的二进制序列在雷达，声纳和通信系统中引起关注。在本文中，我们证明了n = 2 ^k的n − 1的Rudin–Shapiro多项式的Mahler测度是渐近（2 n / e）^1/2的，这是B. Saffari在1985年提出的。很大程度上基于B. Rodgers最近证明的Saffari和Montgomery猜想。