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arXiv · 2606.06669

The Sidon Decomposition Problem in Abelian Groups of Bounded Torsion

Mark Lewko
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Abstract

Let $G$ be a compact abelian group whose dual group $\Gamma=\widehat{G}$ has bounded torsion. In 1967, Malliavin-Brameret and Malliavin proved that every Sidon set in $\Gamma$ is a finite union of quasi-independent sets when $\Gamma$ has prime exponent. This was later extended to squarefree exponents in work of Varopoulos and Bourgain. We prove the remaining bounded-torsion case. Consequently, if $\widehat{G}$ has bounded torsion, then a subset $\Lambda\subset \widehat{G}\setminus{0}$ is Sidon if and only if it is a finite union of quasi-independent sets.

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Mark Lewko. 2026-06-04. The Sidon Decomposition Problem in Abelian Groups of Bounded Torsion. https://arxiv.org/abs/2606.06669

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