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

Stefan Neuwirth

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

Functional Analysis 2026-03-31 v1

Authors: Stefan Neuwirth

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 $c_0+c_1e^{it}+c_2e^{2it}+c_3e^{3it}$ 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.

Keywords

Sidon constant trigonometric polynomial Fourier analysis extremal function Banaschewski set

Cite

@article{arxiv.2603.28229,
  title  = {On the (Fourier analytic) Sidon constant of {0,1,2,3}},
  author = {Stefan Neuwirth},
  journal= {arXiv preprint arXiv:2603.28229},
  year   = {2026}
}

Comments

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

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

Abstract

Keywords

Cite

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