The Rudin-Shapiro polynomials and The Fekete polynomials are not Lα-flat
Abdalaoui, El Houcein El
Dynamical Systems
Combinatorics
Complex Variables
Number Theory
Spectral Theory
42A05, 42A55 (Primary), 37A05, 37A30 (Secondary)
Original · EN
We establish that the Rudin-Shapiro polynomials are not Lα-flat, for any α≥ 0. We further prove that the "truncated" Rudin-Shapiro sequence cannot generate a sequence of Lα-flat polynomials, for any α≥ 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 Lα-flat, for any α≥ 0.
English translation
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