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

TL;DR

This paper discusses the challenging problem of determining the Fourier analytic Sidon constant for four-term trigonometric polynomials, exploring ideas for its computation and extremal functions.

Contribution

It introduces new ideas for calculating the Sidon constant for four-term polynomials and describes a special torus of extremal functions.

Findings

Proposes methods to estimate the Sidon constant.

Identifies a distinguished torus of extremal functions.

Provides insights into the structure of extremal polynomials.

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.