Rudin-Shapiro多项式的Mahler测度的渐近值
The asymptotic value of the Mahler measure of the Rudin-Shapiro polynomials
摘要：
在信号处理中，Rudin-Shapiro多项式具有良好的自相关特性，并且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、声纳和通信系统中具有重要意义。本文证明了$n=2^k-1$次Rudin-Shapiro多项式的Mahler测度是渐近的$(2n/e)^{1/2}$，正如B. 1985年的萨法里。我们的方法主要基于最近由B.罗杰斯
英文摘要：
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 $n=2^k-1$ 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.
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