On the (Fourier analytic) Sidon constant of {0,1,2,3}

Stefan Neuwirth

paper

On the (Fourier analytic) Sidon constant of {0,1,2,3}

arXiv:2603.28229

Abstract

This constant is the maximum of the sum $∣ c_{0} ∣ + ∣ c_{1} ∣ + ∣ c_{2} ∣ + ∣ c_{3} ∣$ of the moduli of the coefficients of a trigonometric polynomial $c_{0} + c_{1} e^{i t} + c_{2} e^{2 i t} + c_{3} e^{3 i t}$ bounded by 1. Its value is still unknown, but I will present some ideas on how to compute it and describe a distinguished torus of extremal functions.

4th Workshop on Fourier Analysis and Related Fields, Imre Z. Ruzsa; Szil{á}rd R{é}v{é}sz; Mate Matolcsi, Aug 2013, Budapest, Hungary