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

Stefan Neuwirth

doi:10.48550/arxiv.2603.28229

March 30, 2026Open Access

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

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Key Points

The aim is to investigate the Sidon constant for the set {0,1,2,3} and contribute ideas for its computation.
Analyze the sum of moduli of coefficients in bounded trigonometric polynomials.
Discuss properties of extremal functions through geometric perspectives.
The exact value of the Sidon constant remains unknown.
Insights into potential methods for computing the constant are presented.

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Implication

This analysis highlights the Sidon constant related to trigonometric polynomials and its unexplored value.

Abstract

This constant is the maximum of the sum |c₀|+|c₁|+|c₂|+|c₃| of the moduli of the coefficients of a trigonometric polynomial c₀+c₁eⁱᵗ+c₂e²ⁱᵗ+c₃e³ⁱᵗ 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.

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Stefan Neuwirth (2026) studied this question.

synapsesocial.com/papers/69d1fb20a79560c99a0a1913 https://doi.org/10.48550/arxiv.2603.28229

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

Key Points

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Implication

Abstract

Discussion

Cite This Study

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

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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