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arXiv · 1603.04095

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

El Houcein El Abdalaoui
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Abstract

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

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El Houcein El Abdalaoui. 2016-03-13. The Rudin-Shapiro polynomials and The Fekete polynomials are not $L^\alpha$-flat. https://arxiv.org/abs/1603.04095

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