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We establish that the Rudin-Shapiro polynomials are not $L^\alpha$-flat, forany $\alpha \geq 0$. We further prove that the "truncated" Rudin-Shapirosequence 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 thatthe Fekete polynomials and the modified or shifted Fekete polynomials are not$L^\alpha$-flat, for any $\alpha \geq 0$.

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