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arXiv 1603.04095math.DSmath.COmath.CVmath.NTmath.SP
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Rudin-Shapiro多项式和Fekete多项式不是$L^α$平坦的

The Rudin-Shapiro polynomials and The Fekete polynomials are not $L^α$-flat

El Houcein El Abdalaoui

备注：
In this new version, minor misprints are corrected. The author further announce that he establishes a one-to-one correspondence between the L^2-normalized Littlewood polynomials and Bourgain-Newman polynomials. As a consequence he proved a criterion for L^1-flatness fro which he can deduce that the Littlewood polynomials are not L^α-flat if the frequency of 1 is not between 1/4 and 3/4
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摘要：

我们建立了Rudin-Shapiro多项式不是$L^α$平坦的，对于任何$α\geq 0$。进一步证明了对于任何$α\geq 0$，“截断”Rudin-Shapiro序列都不能生成$L^α$ -平坦多项式序列.在附录中，我们提出了一个简单的证明的事实，即Fekete多项式和修改或移位的Fekete多项式不是$L^α$ -平坦的，任何$α\geq 0$。

英文摘要：

We establish that the Rudin-Shapiro polynomials are not $L^α$-flat, for any $α\geq 0$. We further prove that the "truncated" Rudin-Shapiro sequence cannot generate a sequence of $L^α$-flat polynomials, for any $α\geq 0$. In the appendix, we present a simple proof of the fact that the Fekete polynomials and the modified or shifted Fekete polynomials are not $L^α$-flat, for any $α\geq 0$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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